Journal articles: 'THERMOFIELD DOUBLE'

1

Guo, Xiao-Kan. "Thermofield double states in group field theory." International Journal of Modern Physics A 36, no. 02 (January 20, 2021): 2150008. http://dx.doi.org/10.1142/s0217751x21500081.

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Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a “thermal” vacuum respecting the Kubo–Martin–Schwinger condition. We work with the Weyl [Formula: see text]-algebra of group fields, and a particular type of thermofield double states with single type of symmetry is obtained from the squeezed states on this Weyl algebra. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter [Formula: see text]. We suggest that the equilibrium flow parameters [Formula: see text] of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.

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Jevicki, Antal, Xianlong Liu, Junggi Yoon, and Junjie Zheng. "Dynamical Symmetry and the Thermofield State at Large N." Universe 8, no. 2 (February 10, 2022): 114. http://dx.doi.org/10.3390/universe8020114.

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We discuss thermofield double QFT at real time, in the large N limit. First, we establish a (dynamical) symmetry, which we argue holds in general for the real-time portion of the Schwinger–Kelydish contour. At large N, this symmetry is seen to generate a one-parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on an example of the O(N) vector QFT. As a nontrivial application, we describe the construction of the corresponding (large N) thermofield double state in real-time collective formalism.

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Zhu, D., S. Johri, N. M. Linke, K. A. Landsman, C. Huerta Alderete, N. H. Nguyen, A. Y. Matsuura, T. H. Hsieh, and C. Monroe. "Generation of thermofield double states and critical ground states with a quantum computer." Proceedings of the National Academy of Sciences 117, no. 41 (September 28, 2020): 25402–6. http://dx.doi.org/10.1073/pnas.2006337117.

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Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum–classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.

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Sundar, Bhuvanesh, Andreas Elben, Lata Kh Joshi, and Torsten V. Zache. "Proposal for measuring out-of-time-ordered correlators at finite temperature with coupled spin chains." New Journal of Physics 24, no. 2 (February 1, 2022): 023037. http://dx.doi.org/10.1088/1367-2630/ac5002.

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Abstract Information scrambling, which is the spread of local information through a system’s many-body degrees of freedom, is an intrinsic feature of many-body dynamics. In quantum systems, the out-of-time-ordered correlator (OTOC) quantifies information scrambling. Motivated by experiments that have measured the OTOC at infinite temperature and a theory proposal to measure the OTOC at finite temperature using the thermofield double state, we describe a protocol to measure the OTOC in a finite temperature spin chain that is realized approximately as one half of the ground state of two moderately-sized coupled spin chains. We consider a spin Hamiltonian with particle–hole symmetry, for which we show that the OTOC can be measured without needing sign-reversal of the Hamiltonian. We describe a protocol to mitigate errors in the estimated OTOC, arising from the finite approximation of the system to the thermofield double state. We show that our protocol is also robust to main sources of decoherence in experiments.

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5

del Campo, A., J. Molina-Vilaplana, L. F. Santos, and J. Sonner. "Decay of a thermofield-double state in chaotic quantum systems." European Physical Journal Special Topics 227, no. 3-4 (September 2018): 247–58. http://dx.doi.org/10.1140/epjst/e2018-00083-5.

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6

Narayan, K. "de Sitter entropy as entanglement." International Journal of Modern Physics D 28, no. 14 (October 2019): 1944019. http://dx.doi.org/10.1142/s021827181944019x.

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We describe connected timelike codim-2 extremal surfaces stretching between the future and the past boundaries in the static patch coordinatization of de Sitter space. These are analogous to rotated versions of certain surfaces in the AdS black hole. The existence of these surfaces via the [Formula: see text] framework suggests the speculation that [Formula: see text] is dual to two copies of ghost-like CFTs in a thermofield-double-type entangled state. In studies of entanglement in ghost systems and “ghost-spin” chains, we show that similar entangled states in two copies of ghost-spin ensembles always have positive norm and positive entanglement.

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Chenu, Aurélia, Javier Molina-Vilaplana, and Adolfo del Campo. "Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems." Quantum 3 (March 4, 2019): 127. http://dx.doi.org/10.22331/q-2019-03-04-127.

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Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.

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Ghaffarnejad, Hossein, Mohammad Farsam, and Emad Yaraie. "Effects of Quintessence Dark Energy on the Action Growth and Butterfly Velocity." Advances in High Energy Physics 2020 (January 20, 2020): 1–7. http://dx.doi.org/10.1155/2020/9529356.

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In this work we are about to investigate the effects of quintessence dark energy on evolution of the computational complexity relating to the AdS/CFT correspondence. We use “complexity=action” conjecture for a charged AdS black hole surrounded by the dark energy at the quintessence regime. Then we try to find some conditions on the quintessence parameters where the Lloyd bound is satisfied in presence of affects of the quintessence dark energy on the complexity growth at the late time approximations. We compare late time approximation of the action growth by perturbed geometry in small limits of shift function. Actually we investigate the evµolution of complexity when thermofield double state on the boundaries is perturbed by local operator corresponding to a shock wave geometry as holographically. Furthermore we seek spread of local shock wave on the black hole horizon in presence of the quintessence dark energy.

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Anand, Namit, and Paolo Zanardi. "BROTOCs and Quantum Information Scrambling at Finite Temperature." Quantum 6 (June 23, 2022): 744. http://dx.doi.org/10.22331/q-2022-06-23-744.

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Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

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Anand, Namit, and Paolo Zanardi. "BROTOCs and Quantum Information Scrambling at Finite Temperature." Quantum 6 (June 27, 2022): 746. http://dx.doi.org/10.22331/q-2022-06-27-746.

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Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

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11

Sohal, Ramanjit, Laimei Nie, Xiao-Qi Sun, and Eduardo Fradkin. "Thermalization of randomly coupled SYK models." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (January 1, 2022): 013103. http://dx.doi.org/10.1088/1742-5468/ac416b.

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Abstract We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-N limit. Using numerical large-N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

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12

Vancea, Ion V. "Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space." Advances in High Energy Physics 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/3706870.

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The two-dimensional σ-model with the de Sitter target space is locally canonic in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the cylindrical base space are entangled among themselves and interact with the de Sitter metric. Firstly, we show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations constrained by the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the nonequilibrium thermofield dynamics formalism. The thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. From these we compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the σ-model equations of motion, and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields.

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13

Dadras, Pouria. "Disentangling the thermofield-double state." Journal of High Energy Physics 2022, no. 1 (January 2022). http://dx.doi.org/10.1007/jhep01(2022)075.

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Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

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14

Chapman, Shira, and Hong Zhe (Vincent) Chen. "Charged complexity and the thermofield double state." Journal of High Energy Physics 2021, no. 2 (February 2021). http://dx.doi.org/10.1007/jhep02(2021)187.

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Abstract We establish a systematic framework for studying quantum computational complexity of Gaussian states of charged systems based on Nielsen’s geometric approach. We use this framework to examine the effect of a chemical potential on the dynamics of complexity. As an example, we consider the complexity of a charged thermofield double state constructed from two free massive complex scalar fields in the presence of a chemical potential. We show that this state factorizes between positively and negatively charged modes and demonstrate that this fact can be used to relate it, for each momentum mode separately, to two uncharged thermofield double states with shifted temperatures and times. We evaluate the complexity of formation for the charged thermofield double state, both numerically and in certain analytic expansions. We further present numerical results for the time dependence of complexity. We compare various aspects of these results to those obtained in holography for charged black holes.

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15

Lin, Cheng-Ju, Zhi Li, and Timothy H. Hsieh. "Entanglement Renormalization of Thermofield Double States." Physical Review Letters 127, no. 8 (August 17, 2021). http://dx.doi.org/10.1103/physrevlett.127.080602.

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16

Doroudiani, Mehregan, Ali Naseh, and Reza Pirmoradian. "Complexity for charged thermofield double states." Journal of High Energy Physics 2020, no. 1 (January 2020). http://dx.doi.org/10.1007/jhep01(2020)120.

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17

Jiang, Jie, and Xiangjing Liu. "Circuit complexity for fermionic thermofield double states." Physical Review D 99, no. 2 (January 17, 2019). http://dx.doi.org/10.1103/physrevd.99.026011.

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18

Chapman, Shira, Jens Eisert, Lucas Hackl, Michal P. Heller, Ro Jefferson, Hugo Marrochio, and Robert C. Myers. "Complexity and entanglement for thermofield double states." SciPost Physics 6, no. 3 (March 15, 2019). http://dx.doi.org/10.21468/scipostphys.6.3.034.

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Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t = 0t=0, we show that the complexity of formation is proportional to the thermodynamic entropy, in qualitative agreement with holographic complexity proposals. For TFD states at t>0t>0, we demonstrate that the complexity evolves in time and saturates after a time of the order of the inverse temperature. The latter feature, which is in contrast with the results of holographic proposals, is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel technical aspect of our work is framing complexity calculations in the language of covariance matrices and the associated symplectic transformations, which provide a natural language for dealing with Gaussian states. Furthermore, for free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with the time dependence of the entanglement entropy for simple bipartitions of TFDs. We relate our results for the entanglement entropy to previous studies on non-equilibrium entanglement evolution following quenches. We also present a new analytic derivation of a logarithmic contribution due to the zero momentum mode in the limit of vanishing mass for a subsystem containing a single degree of freedom on each side of the TFD and argue why a similar logarithmic growth should be present for larger subsystems.

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Cottrell, William, Ben Freivogel, Diego M. Hofman, and Sagar F. Lokhande. "How to build the thermofield double state." Journal of High Energy Physics 2019, no. 2 (February 2019). http://dx.doi.org/10.1007/jhep02(2019)058.

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20

Wu, Jingxiang, and Timothy H. Hsieh. "Variational Thermal Quantum Simulation via Thermofield Double States." Physical Review Letters 123, no. 22 (November 26, 2019). http://dx.doi.org/10.1103/physrevlett.123.220502.

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21

Berenstein, David. "Quenches on thermofield double states and time reversal symmetry." Physical Review D 100, no. 6 (September 23, 2019). http://dx.doi.org/10.1103/physrevd.100.066022.

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22

Ghasemi, Mostafa, Ali Naseh, and Reza Pirmoradian. "Odd entanglement entropy and logarithmic negativity for thermofield double states." Journal of High Energy Physics 2021, no. 10 (October 2021). http://dx.doi.org/10.1007/jhep10(2021)128.

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Abstract We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times t < β/2 (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times t < d/2 (half of the distance between intervals). We also find a similar delay to see linear growth of ∆S = SOEE− SEE. All these results show that the dynamics of these measures are consistent with the quasi-particle picture, of course apart from the logarithmic growth.

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23

Antonini, Stefano, Brianna Grado-White, Shao-Kai Jian, and Brian Swingle. "Holographic measurement and quantum teleportation in the SYK thermofield double." Journal of High Energy Physics 2023, no. 2 (February 9, 2023). http://dx.doi.org/10.1007/jhep02(2023)095.

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Abstract According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the Sachdev-Ye-Kitaev (SYK) model’s thermofield double state, dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate the (Renyi-2) mutual information between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the von Neumann entropy. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of traversable wormholes.

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Anempodistov, P. A. "Remarks on the thermofield double state in 4D black hole background." Physical Review D 103, no. 10 (May 14, 2021). http://dx.doi.org/10.1103/physrevd.103.105008.

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Yang, Run-Qiu, Cheng-Yong Zhang, and Wen-Ming Li. "Holographic entanglement of purification for thermofield double states and thermal quench." Journal of High Energy Physics 2019, no. 1 (January 2019). http://dx.doi.org/10.1007/jhep01(2019)114.

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26

Arzano, Michele. "Vacuum thermal effects in flat space-time from conformal quantum mechanics." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)003.

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Abstract The generators of radial conformal symmetries in Minkowski space-time can be mapped to the generators of time evolution in conformal quantum mechanics. Within this correspondence we show that in conformal quantum mechanics the state associated to the inertial vacuum in Minkowski space-time has the structure of a thermofield double. Such state is built from a bipartite “vacuum state”, the ground state of the generators of hyperbolic time evolution, which cover only part of the time domain. When time evolution is restricted to a finite time domain one obtains the temperature perceived by static diamond observers in the Minkowski vacuum. When time evolution is determined by dilations, covering only half of the time line, the temperature of the thermofield double corresponds to the non-vanishing temperature perceived by Milne observers whose proper time evolution is confined to the future cone (Milne universe) of Minkowski space-time. The two pictures are related by a conformal transformation on the real line. Our result provides a purely group theoretical derivation of the Milne and diamond temperatures and shows that the fundamental ingredient for vacuum thermal effects is the presence of a horizon rather than acceleration.

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Li, Ze, and Run-Qiu Yang. "Upper bounds of holographic entanglement entropy growth rate for thermofield double states." Journal of High Energy Physics 2022, no. 10 (October 11, 2022). http://dx.doi.org/10.1007/jhep10(2022)072.

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Abstract We studied the upper bounds of the holographic entanglement entropy growth rate for thermofield double (TFD) states. By comparing the cases of vacuum AdS and charged AdS black holes, we conjecture: for all static planar or spherically symmetric asymptotically Schwarzschild-AdS black holes of same mass density or entropy density, the vacuum AdS black hole gives the maximum entanglement entropy growth rate. We gave proofs by assuming dominant energy condition. We also considered the AdS black hole spacetime with real scalar fields case, where the scalar fields violate the dominant energy condition and the bulk geometry is not asymptotically Schwarzschild-AdS. Numerical results show that this case vacuum black hole still has maximal growth rate if we fixed entropy. However, in the case of fixed energy, vacuum case has maximal growth rate of entanglement entropy only under standard quantization scheme.

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Yang, Run-Qiu. "Complexity for quantum field theory states and applications to thermofield double states." Physical Review D 97, no. 6 (March 7, 2018). http://dx.doi.org/10.1103/physrevd.97.066004.

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Su, Vincent Paul. "Variational preparation of the thermofield double state of the Sachdev-Ye-Kitaev model." Physical Review A 104, no. 1 (July 29, 2021). http://dx.doi.org/10.1103/physreva.104.012427.

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Yang, Run-Qiu, Chao Niu, Cheng-Yong Zhang, and Keun-Young Kim. "Comparison of holographic and field theoretic complexities for time dependent thermofield double states." Journal of High Energy Physics 2018, no. 2 (February 2018). http://dx.doi.org/10.1007/jhep02(2018)082.

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Lensky, Yuri D., and Xiao-Liang Qi. "Rescuing a black hole in the large-q coupled SYK model." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)116.

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Abstract In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-q theory with the bulk low energy effective theory. In particular, we study the special case of a “rescued black hole”, which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS2 vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-q and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.

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Zou, Yijian, and Guifre Vidal. "Multiboundary generalization of thermofield double states and their realization in critical quantum spin chains." Physical Review B 105, no. 12 (March 21, 2022). http://dx.doi.org/10.1103/physrevb.105.125125.

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Mounim, Ayoub, and Wolfgang Mück. "Reparameterization dependence is useful for holographic complexity." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)010.

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Abstract Holographic complexity in the “complexity equals action” approach is reconsidered relaxing the requirement of reparameterization invariance of the action with the prescription that the action vanish in any static, vacuum causal diamond. This implies that vacuum anti-de Sitter space plays the role of the reference state. Moreover, the complexity of an anti-de Sitter-Schwarzschild black hole becomes intrinsically finite and saturates Lloyd’s bound after a critical time. It is also argued that several artifacts, such as the unphysical negative-time interval, can be removed by truly considering the bulk dual of the thermofield double state.

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Jefferson, Ro. "Comments on black hole interiors and modular inclusions." SciPost Physics 6, no. 4 (April 5, 2019). http://dx.doi.org/10.21468/scipostphys.6.4.042.

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We show how the traversable wormhole induced by a double-trace deformation of the thermofield double state can be understood as a modular inclusion of the algebras of exterior operators. The effect of this deformation is the creation of a new region of spacetime deep in the bulk, corresponding to a non-trivial center between the left and right algebras. This set-up provides a precise framework for investigating how black hole interiors are encoded in the CFT. In particular, we use modular theory to demonstrate that state dependence is an inevitable feature of any attempt to represent operators behind the horizon. Building on this geometrical structure, we propose that modular inclusions may provide a more precise means of investigating the nascent relationship between entanglement and geometry in the context of the emergent spacetime paradigm.

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Gu, Yingfei, Alexei Kitaev, and Pengfei Zhang. "A two-way approach to out-of-time-order correlators." Journal of High Energy Physics 2022, no. 3 (March 2022). http://dx.doi.org/10.1007/jhep03(2022)133.

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Abstract Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-N systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour. We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time. These dynamical perturbations, or scrambling modes, are considered on the thermofield double background and decomposed into a coherent and an incoherent part. For the large-q SYK, we obtain the OTOC in a closed form. We also prove a previously conjectured relation between the Lyapunov exponent and high-frequency behavior of the spectral function.

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Al Balushi, Abdulrahim, Zhencheng Wang, and Donald Marolf. "Traversability of multi-boundary wormholes." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)083.

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Abstract We generalize the Gao-Jafferis-Wall construction of traversable two-sided wormholes to multi-boundary wormholes. In our construction, we take the background spacetime to be multi-boundary black holes in AdS3. We work in the hot limit where the dual CFT state in certain regions locally resembles the thermofield double state. Furthermore, in these regions, the hot limit makes the causal shadow exponentially small. Based on these two features of the hot limit, and with the three-boundary wormhole as our main example, we show that traversability between any two asymptotic regions in a multi-boundary wormhole can be triggered using a double-trace deformation. In particular, the two boundary regions need not have the same temperature and angular momentum. We discuss the non-trivial angular dependence of traversability in our construction, as well as the effect of the causal shadow region.

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Sagastizabal, R., S. P. Premaratne, B. A. Klaver, M. A. Rol, V. Negîrneac, M. S. Moreira, X. Zou, et al. "Variational preparation of finite-temperature states on a quantum computer." npj Quantum Information 7, no. 1 (August 20, 2021). http://dx.doi.org/10.1038/s41534-021-00468-1.

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AbstractThe preparation of thermal equilibrium states is important for the simulation of condensed matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators and demonstrate this technique experimentally using a gate-based quantum processor. Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation. The fidelity of generated states to the thermal-equilibrium state smoothly varies from 99 to 75% between infinite and near-zero simulated temperature, in quantitative agreement with numerical simulations of the noisy quantum processor with error parameters drawn from experiment.

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38

Horowitz, Gary T., Henry Leung, Leonel Queimada, and Ying Zhao. "Bouncing inside the horizon and scrambling delays." Journal of High Energy Physics 2022, no. 11 (November 7, 2022). http://dx.doi.org/10.1007/jhep11(2022)025.

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Abstract We study charged perturbations of the thermofield double state dual to a charged AdS black hole. We model the perturbation by a massless charged shell in the bulk. Unlike the neutral case, all such shells bounce at a definite radius, which can be behind the horizon. We show that the standard “shock wave” calculation of a scrambling time indicates that adding charge increases the scrambling time. We then give two arguments using the bounce that suggest that scrambling does not actually take longer when charge is added, but instead its onset is delayed. We also construct a boundary four point function which detects whether the shell bounces inside the black hole.

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39

Zhang, Pengfei. "More on complex Sachdev-Ye-Kitaev eternal wormholes." Journal of High Energy Physics 2021, no. 3 (March 2021). http://dx.doi.org/10.1007/jhep03(2021)087.

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Abstract In this work, we study a generalization of the coupled Sachdev-Ye-Kitaev (SYK) model with U(1) charge conservations. The model contains two copies of the complex SYK model at different chemical potentials, coupled by a direct hopping term. In the zero-temperature and small coupling limit with small averaged chemical potential, the ground state is an eternal wormhole connecting two sides, with a specific charge Q = 0, which is equivalent to a thermofield double state. We derive the conformal Green’s functions and determine corresponding IR parameters. At higher chemical potential, the system transit into the black hole phase. We further derive the Schwarzian effective action and study its quench dynamics. Finally, we compare numerical results with the analytical predictions.

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Maldacena, Juan, and Alexey Milekhin. "SYK wormhole formation in real time." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)258.

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Abstract We study the real time formation of the ground state of two coupled SYK models. This is a highly entangled state which is close to the thermofield double state and can be viewed as a wormhole. We start from a high temperature state, we let it cool by coupling to a cold bath. We numerically solve for the large N dynamics. Our main result is that the system forms a wormhole by going through a region with negative specific heat, taking time that is independent of N. The dynamics is smooth everywhere and it seems to follow the equilibrium thermodynamic configurations of the microcanonical ensemble. Also we comment on the relation between this coupled SYK model and Jackiw-Teitelboim gravity theory with bulk fields.

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41

Aalsma, L., A. Cole, E. Morvan, J. P. van der Schaar, and G. Shiu. "Shocks and information exchange in de Sitter space." Journal of High Energy Physics 2021, no. 10 (October 2021). http://dx.doi.org/10.1007/jhep10(2021)104.

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Abstract We discuss some implications of recent progress in understanding the black hole information paradox for complementarity in de Sitter space. Extending recent work by two of the authors, we describe a bulk procedure that allows information expelled through the cosmological horizon to be received by an antipodal observer. Generically, this information transfer takes a scrambling time t = H−1 log(SdS). We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static patches. The procedure also requires the presence of an (entangled) energy reservoir, created by the collection of Hawking modes from the cosmological horizon. We show how this procedure avoids a cloning paradox and comment on its implications.

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42

Balasubramanian, Vijay, Matthew DeCross, and Gábor Sárosi. "Knitting wormholes by entanglement in supergravity." Journal of High Energy Physics 2020, no. 11 (November 2020). http://dx.doi.org/10.1007/jhep11(2020)167.

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Abstract We construct a single-boundary wormhole geometry in type IIB supergravity by perturbing two stacks of N extremal D3-branes in the decoupling limit. The solution interpolates from a two-sided planar AdS-Schwarzschild geometry in the interior, through a harmonic two-center solution in the intermediate region, to an asymptotic AdS space. The construction involves a CPT twist in the gluing of the wormhole to the exterior throats that gives a global monodromy to some coordinates, while preserving orientability. The geometry has a dual interpretation in $$ \mathcal{N} $$ N = 4 SU(2N) Super Yang-Mills theory in terms of a Higgsed SU(2N) → S(U(N) × U(N)) theory in which $$ \mathcal{O} $$ O (N2) degrees of freedom in each SU(N) sector are entangled in an approximate thermofield double state at a temperature much colder than the Higgs scale. We argue that the solution can be made long-lived by appropriate choice of parameters, and comment on mechanisms for generating traversability. We also describe a construction of a double wormhole between two universes.

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Balasubramanian, Vijay, Arjun Kar, and Tomonori Ugajin. "Entanglement between two disjoint universes." Journal of High Energy Physics 2021, no. 2 (February 2021). http://dx.doi.org/10.1007/jhep02(2021)136.

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Abstract We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an “island” on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to show that this island coincides with a causal shadow region that is created by the entanglement in the gravitating geometry. At high entanglement temperatures, the island contribution to the entropy functional leads to a bound on entanglement entropy, analogous to the Page behavior of evaporating black holes. We demonstrate that the entanglement wedge of the non-gravitating universe grows with the entanglement temperature until, eventually, the gravitating universe can be entirely reconstructed from the non-gravitating one.

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Wang, Qing-Bing, Ming-Hui Yu, and Xian-Hui Ge. "Scrambling time for analogue black holes embedded in AdS space." European Physical Journal C 82, no. 5 (May 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10438-2.

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AbstractWe propose a gedanken experiment on realizing thermofield double state (TFD) by using analog black holes and provide an approach to test the scrambling time. Through this approach, we demonstrate clearly how shock wave changes the TFD state as time evolves. As the whole system evolves forward in time, the perturbation of space-time geometry will increase exponentially. Finally, it will destroy the entanglement between the two states of the thermal field, and the mutual information between them is reduced to zero in the time scale of scrambling. The results show that for perturbations of analogue black holes embedded in AdS space, the scale of the scrambling time is closely related to the logarithm of entropy of the black hole. The results provide further theoretical argument for the scrambling time, which can be further falsified in experiments.

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Hollowood, Timothy J., S. Prem Kumar, Andrea Legramandi, and Neil Talwar. "Ephemeral islands, plunging quantum extremal surfaces and BCFT channels." Journal of High Energy Physics 2022, no. 1 (January 2022). http://dx.doi.org/10.1007/jhep01(2022)078.

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Abstract We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a special class of disconnected OPE channels. The quantum extremal surfaces start inside the horizon, but can emerge from and plunge back inside as time evolves, accompanied by a characteristic dip in the entropy also seen in the free fermion BCFT. Finally an entropy equilibrium is reached with a no-island saddle.

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Ageev, Dmitry S. "Shaping contours of entanglement islands in BCFT." Journal of High Energy Physics 2022, no. 3 (March 2022). http://dx.doi.org/10.1007/jhep03(2022)033.

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Abstract In this paper, we study the fine structure of entanglement in holographic two-dimensional boundary conformal field theories (BCFT) in terms of the spatially resolved quasilocal extension of entanglement entropy — entanglement contour. We find that the boundary induces discontinuities in the contour revealing hidden localization-delocalization patterns of the entanglement degrees of freedom. Moreover, we observe the formation of “islands” where the entanglement contour vanishes identically implying that these regions do not contribute to the entanglement at all. We argue that these phenomena are the manifestation of the entanglement islands recently discussed in the literature. We apply the entanglement contour proposal to the recently discussed BCFT black hole models reproducing the Page curve — moving mirror model and the pair of BCFT in the thermofield double state. From the viewpoint of entanglement contour, the Page curve also carries the imprint of strong delocalization caused by dynamical entanglement islands.

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Magán, Javier M. "Proof of the universal density of charged states in QFT." Journal of High Energy Physics 2021, no. 12 (December 2021). http://dx.doi.org/10.1007/jhep12(2021)100.

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Abstract We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

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48

Belin, Alexandre, Robert C. Myers, Shan-Ming Ruan, Gábor Sárosi, and Antony J. Speranza. "Complexity equals anything II." Journal of High Energy Physics 2023, no. 1 (January 26, 2023). http://dx.doi.org/10.1007/jhep01(2023)154.

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Abstract We expand on our results in [1] to present a broad new class of gravitational observables in asymptotically Anti-de Sitter space living on general codimension-zero regions of the bulk spacetime. By taking distinct limits, these observables can reduce to well-studied holographic complexity proposals, e.g., the volume of the maximal slice and the action or spacetime volume of the Wheeler-DeWitt patch. As with the codimension-one family found in [1], these new observables display two key universal features for the thermofield double state: they grow linearly in time at late times and reproduce the switchback effect. Hence we argue that any member of this new class of observables is an equally viable candidate as a gravitational dual of complexity. Moreover, using the Peierls construction, we show that variations of the codimension-zero and codimension-one observables are encoded in the gravitational symplectic form on the semi-classical phase-space, which can then be mapped to the CFT.

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Gharibyan, Hrant, Masanori Hanada, Masazumi Honda, and Junyu Liu. "Toward simulating superstring/M-theory on a quantum computer." Journal of High Energy Physics 2021, no. 7 (July 2021). http://dx.doi.org/10.1007/jhep07(2021)140.

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Abstract We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. Our prescription consists of four steps: regularization of the Hilbert space, adiabatic state preparation, simulation of real-time dynamics, and measurements. Regularization is performed for the BMN matrix model with the introduction of energy cut-off via the truncation in the Fock space. We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state. Then, we provide an explicit construction for simulating real-time dynamics utilizing techniques of block-encoding, qubitization, and quantum signal processing. Lastly, we present a set of measurements and experiments that can be carried out on a quantum computer to further our understanding of superstring/M-theory beyond analytic results.

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Jafferis, Daniel Louis, and Elliot Schneider. "Stringy ER = EPR." Journal of High Energy Physics 2022, no. 10 (October 31, 2022). http://dx.doi.org/10.1007/jhep10(2022)195.

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Abstract The ER = EPR correspondence relates a superposition of entangled, disconnected spacetimes to a connected spacetime with an Einstein-Rosen bridge. We construct examples in which both sides may be described by weakly-coupled string theory. The relation between them is given by a Lorentzian continuation of the FZZ duality of the two-dimensional Euclidean black hole CFT in one example, and in another example by continuation of a similar duality that we propose for the asymptotic Euclidean AdS3 black hole. This gives a microscopic understanding of ER = EPR: one has a worldsheet duality between string theory in a connected, eternal black hole, and in a superposition of disconnected geometries in an entangled state. The disconnected description includes a condensate of entangled folded strings emanating from a strong-coupling region in place of a bifurcation point. Our construction relies on a Lorentzian interpretation of Euclidean time winding operators via angular quantization, as well as some lesser known worldsheet string theories, such as perturbation theory around a thermofield-double state, which we define using Schwinger-Keldysh contours in target space.

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Journal articles on the topic 'THERMOFIELD DOUBLE'

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