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Artykuły w czasopismach na temat „Aubry-André-Harper model”

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Data publikacji: 6 września 2023

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1

Chen, Chao, Lu Qi, Yan Xing, Wen-Xue Cui, Shou Zhang, and Hong-Fu Wang. "General bounded corner states in two-dimensional off-diagonal Aubry–André–Harper model with flat bands." New Journal of Physics 23, no. 12 (2021): 123008. http://dx.doi.org/10.1088/1367-2630/ac38cc.

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Abstract We investigate the general bounded corner states in a two-dimensional off-diagonal Aubry–André–Harper square lattice model supporting flat bands. We show that for certain values of the nearest-neighbor hopping amplitudes, triply degenerate zero-energy flat bands emerge in this lattice system. Moreover, the two-dimensional off-diagonal Aubry–André–Harper model splits into isolated fragments and hosts some general bounded corner states, and the absence of the energy gap results in that these general bounded corner states are susceptible to disorder. By adding intracellular next-nearest-neighbor hoppings, two flat bands with opposite energies split off from the original triply degenerate zero-energy flat bands and some robust general bounded corner states appear in real-space energy spectrum. Our work shows a way to obtain robust general bounded corner states in the two-dimensional off-diagonal Aubry–André–Harper model by the intracellular next-nearest-neighbor hoppings.

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2

Li, Yi, Jia-Hui Zhang, Feng Mei, Jie Ma, Liantuan Xiao, and Suotang Jia. "Generalized Aubry–André–Harper Models in Optical Superlattices." Chinese Physics Letters 39, no. 6 (2022): 063701. http://dx.doi.org/10.1088/0256-307x/39/6/063701.

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Ultracold atoms trapped in optical superlattices provide a simple platform for realizing the seminal Aubry–André–Harper (AAH) model. However, this model ignores the periodic modulations on the nearest-neighbor hoppings. We establish a generalized AAH model by which an optical superlattice system can be approximately described when V 1 ≫ V 2, with periodic modulations on both on-site energies and nearest-neighbor hoppings. This model supports much richer topological properties absent in the standard AAH model. Specifically, by calculating the Chern numbers and topological edge states, we show that the generalized AAH model possesses multifarious topological phases and topological phase transitions, unlike the standard AAH model supporting only a single topological phase. Our findings can uncover more opportunities for using optical superlattices to study topological and localization physics.

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3

Zeng, Qi-Bo, Shu Chen, and Rong Lü. "Quench dynamics in the Aubry–André–Harper model with p-wave superconductivity." New Journal of Physics 20, no. 5 (2018): 053012. http://dx.doi.org/10.1088/1367-2630/aabe39.

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4

Sarkar, Manik, Santanu K. Maiti, and Moumita Dey. "Localization phenomena and electronic transport in irradiated Aubry–André–Harper systems." Journal of Physics: Condensed Matter 34, no. 19 (2022): 195303. http://dx.doi.org/10.1088/1361-648x/ac53db.

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Abstract The role of light irradiation on electronic localization is critically investigated for the first time in a tight-binding lattice where site energies are modulated in the cosine form following the Aubry–André–Harper (AAH) model. The critical point of transition from delocalized-to-localized phase can be monitored selectively by regulating the light parameters that is extremely useful to have controlled electron transmission across the system. Starting with a strictly one-dimensional (1D) AAH chain, we extend our analysis considering a two-stranded ladder model which brings peculiar signatures in presence of irradiation. Unlike 1D system, AAH ladder exhibits a mixed phase (MP) zone where both extended and localized energy eigenstates co-exist. This is the fundamental requirement to have mobility edge in energy band spectrum. A mathematical description is given for decoupling the irradiated ladder into two effective 1D AAH chains. The underlying mechanism of getting a MP zone relies on the availability of two distinct critical points (CPs) of the decoupled chains, in presence of second-neighbor hopping between the two strands. Using a minimal coupling scheme the effect of light irradiation is incorporated following the Floquet–Bloch ansatz. The localization behaviors of different energy eigenstates are studied by calculating inverse participation ratio, and, are further explained in a more compact way by calculating two-terminal transmission probabilities together with average density of states. Finally, the decoupling procedure is extended for a more general multi-stranded AAH ladders where multiple CPs and thus multiple mobility edges are found. Our analysis may provide a new route of engineering localization properties in similar kind of other fascinating quasiperiodic systems.

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5

Zhao, X. L., Z. C. Shi, C. S. Yu, and X. X. Yi. "Influence of localization transition on dynamical properties for an extended Aubry–André–Harper model." Journal of Physics B: Atomic, Molecular and Optical Physics 50, no. 23 (2017): 235503. http://dx.doi.org/10.1088/1361-6455/aa92df.

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6

Roy, Nilanjan, and Auditya Sharma. "Entanglement entropy and out-of-time-order correlator in the long-range Aubry–André–Harper model." Journal of Physics: Condensed Matter 33, no. 33 (2021): 334001. http://dx.doi.org/10.1088/1361-648x/ac06e9.

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7

Cao, Ji, Yan Xing, Lu Qi, et al. "Simulating and studying the topological properties of generalized commensurate Aubry–André–Harper model with microresonator array." Laser Physics Letters 15, no. 1 (2017): 015211. http://dx.doi.org/10.1088/1612-202x/aa9831.

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8

Li, Yu-Zeng, Fei-Fei Liu, Zheng-Fang Liu, Qing-Ping Wu, and Xian-Bo Xiao. "Lattice even–odd effect controlled zero-energy corner states in commensurate off-diagonal Aubry–André–Harper model." Physica E: Low-dimensional Systems and Nanostructures 141 (July 2022): 115218. http://dx.doi.org/10.1016/j.physe.2022.115218.

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9

Cui, H. T., M. Qin, L. Tang, H. Z. Shen, and X. X. Yi. "Open dynamics in the Aubry-André-Harper model coupled to a finite bath: The influence of localization in the system and dimensionality of bath." Physics Letters A 421 (January 2022): 127778. http://dx.doi.org/10.1016/j.physleta.2021.127778.

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10

Koley, Arpita, Santanu K. Maiti, Laura M. Pérez, Judith Helena Ojeda Silva, and David Laroze. "Possible Routes to Obtain Enhanced Magnetoresistance in a Driven Quantum Heterostructure with a Quasi-Periodic Spacer." Micromachines 12, no. 9 (2021): 1021. http://dx.doi.org/10.3390/mi12091021.

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In this work, we perform a numerical study of magnetoresistance in a one-dimensional quantum heterostructure, where the change in electrical resistance is measured between parallel and antiparallel configurations of magnetic layers. This layered structure also incorporates a non-magnetic spacer, subjected to quasi-periodic potentials, which is centrally clamped between two ferromagnetic layers. The efficiency of the magnetoresistance is further tuned by injecting unpolarized light on top of the two sided magnetic layers. Modulating the characteristic properties of different layers, the value of magnetoresistance can be enhanced significantly. The site energies of the spacer is modified through the well-known Aubry–André and Harper (AAH) potential, and the hopping parameter of magnetic layers is renormalized due to light irradiation. We describe the Hamiltonian of the layered structure within a tight-binding (TB) framework and investigate the transport properties through this nanojunction following Green’s function formalism. The Floquet–Bloch (FB) anstaz within the minimal coupling scheme is introduced to incorporate the effect of light irradiation in TB Hamiltonian. Several interesting features of magnetotransport properties are represented considering the interplay between cosine modulated site energies of the central region and the hopping integral of the magnetic regions that are subjected to light irradiation. Finally, the effect of temperature on magnetoresistance is also investigated to make the model more realistic and suitable for device designing. Our analysis is purely a numerical one, and it leads to some fundamental prescriptions of obtaining enhanced magnetoresistance in multilayered systems.

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11

Roy, Souvik, Santanu K. Maiti, Laura M. Pérez, Judith Helena Ojeda Silva, and David Laroze. "Localization Properties of a Quasiperiodic Ladder under Physical Gain and Loss: Tuning of Critical Points, Mixed-Phase Zone and Mobility Edge." Materials 15, no. 2 (2022): 597. http://dx.doi.org/10.3390/ma15020597.

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We explore the localization properties of a double-stranded ladder within a tight-binding framework where the site energies of different lattice sites are distributed in the cosine form following the Aubry–André–Harper (AAH) model. An imaginary site energy, which can be positive or negative, referred to as physical gain or loss, is included in each of these lattice sites which makes the system a non-Hermitian (NH) one. Depending on the distribution of imaginary site energies, we obtain balanced and imbalanced NH ladders of different types, and for all these cases, we critically investigate localization phenomena. Each ladder can be decoupled into two effective one-dimensional (1D) chains which exhibit two distinct critical points of transition from metallic to insulating (MI) phase. Because of the existence of two distinct critical points, a mixed-phase (MP) zone emerges which yields the possibility of getting a mobility edge (ME). The conducting behaviors of different energy eigenstates are investigated in terms of inverse participation ratio (IPR). The critical points and thus the MP window can be selectively controlled by tuning the strength of the imaginary site energies which brings a new insight into the localization aspect. A brief discussion on phase transition considering a multi-stranded ladder was also given as a general case, to make the present communication a self-contained one. Our theoretical analysis can be utilized to investigate the localization phenomena in different kinds of simple and complex quasicrystals in the presence of physical gain and/or loss.

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12

Zeng, Qi-Bo, Shu Chen, and Rong Lü. "Generalized Aubry-André-Harper model withp-wave superconducting pairing." Physical Review B 94, no. 12 (2016). http://dx.doi.org/10.1103/physrevb.94.125408.

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13

Longhi, Stefano. "Phase transitions in a non-Hermitian Aubry-André-Harper model." Physical Review B 103, no. 5 (2021). http://dx.doi.org/10.1103/physrevb.103.054203.

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14

He, Yu, Shiqi Xia, Dimitris G. Angelakis, Daohong Song, Zhigang Chen, and Daniel Leykam. "Persistent homology analysis of a generalized Aubry-André-Harper model." Physical Review B 106, no. 5 (2022). http://dx.doi.org/10.1103/physrevb.106.054210.

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15

He, Peng, Yu-Guo Liu, Jian-Te Wang, and Shi-Liang Zhu. "Damping transition in an open generalized Aubry-André-Harper model." Physical Review A 105, no. 2 (2022). http://dx.doi.org/10.1103/physreva.105.023311.

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16

Dai, C. M., W. Wang, and X. X. Yi. "Dynamical localization-delocalization crossover in the Aubry-André-Harper model." Physical Review A 98, no. 1 (2018). http://dx.doi.org/10.1103/physreva.98.013635.

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17

Liu, Fangli, Somnath Ghosh, and Y. D. Chong. "Localization and adiabatic pumping in a generalized Aubry-André-Harper model." Physical Review B 91, no. 1 (2015). http://dx.doi.org/10.1103/physrevb.91.014108.

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18

Yoo, Yongchan, Junhyun Lee, and Brian Swingle. "Nonequilibrium steady state phases of the interacting Aubry-André-Harper model." Physical Review B 102, no. 19 (2020). http://dx.doi.org/10.1103/physrevb.102.195142.

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19

Wang, Li, Na Liu, Shu Chen, and Yunbo Zhang. "Quantum walks in the commensurate off-diagonal Aubry-André-Harper model." Physical Review A 95, no. 1 (2017). http://dx.doi.org/10.1103/physreva.95.013619.

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20

Sajid, Muhammad, Muzamil Shah, Niaz Ali Khan, and Munsif Jan. "Quantum walks in an inhomogeneous off-diagonal Aubry-André-Harper model." Physics Letters A, March 2023, 128763. http://dx.doi.org/10.1016/j.physleta.2023.128763.

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21

Roy, Nilanjan, and Auditya Sharma. "Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model." Physical Review B 103, no. 7 (2021). http://dx.doi.org/10.1103/physrevb.103.075124.

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22

Yahyavi, M., B. Hetényi, and B. Tanatar. "Generalized Aubry-André-Harper model with modulated hopping and p -wave pairing." Physical Review B 100, no. 6 (2019). http://dx.doi.org/10.1103/physrevb.100.064202.

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23

Longhi, Stefano. "Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model." Physical Review B 100, no. 12 (2019). http://dx.doi.org/10.1103/physrevb.100.125157.

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24

Kaya, Tuncer. "Aubry–André–Harper model: multifractality analysis versus Landauer conductance for quasicrystal chains." Indian Journal of Physics, June 20, 2023. http://dx.doi.org/10.1007/s12648-023-02810-z.

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25

Žnidarič, Marko. "Comment on “Nonequilibrium steady state phases of the interacting Aubry-André-Harper model”." Physical Review B 103, no. 23 (2021). http://dx.doi.org/10.1103/physrevb.103.237101.

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26

Lv, Ting, Tian-Cheng Yi, Liangsheng Li, Gaoyong Sun, and Wen-Long You. "Quantum criticality and universality in the p -wave-paired Aubry-André-Harper model." Physical Review A 105, no. 1 (2022). http://dx.doi.org/10.1103/physreva.105.013315.

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27

Lv, Ting, Yu-Bin Liu, Tian-Cheng Yi, Liangsheng Li, Maoxin Liu, and Wen-Long You. "Exploring unconventional quantum criticality in the p -wave-paired Aubry-André-Harper model." Physical Review B 106, no. 14 (2022). http://dx.doi.org/10.1103/physrevb.106.144205.

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28

Purkayastha, Archak, Sambuddha Sanyal, Abhishek Dhar, and Manas Kulkarni. "Anomalous transport in the Aubry-André-Harper model in isolated and open systems." Physical Review B 97, no. 17 (2018). http://dx.doi.org/10.1103/physrevb.97.174206.

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29

Wang, Jun, Xia-Ji Liu, Gao Xianlong, and Hui Hu. "Phase diagram of a non-Abelian Aubry-André-Harper model withp-wave superfluidity." Physical Review B 93, no. 10 (2016). http://dx.doi.org/10.1103/physrevb.93.104504.

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30

Bai, Xiao-Dong, Jia Wang, Xia-Ji Liu, Jun Xiong, Fu-Guo Deng, and Hui Hu. "Polaron in a non-Abelian Aubry-André-Harper model with p -wave superfluidity." Physical Review A 98, no. 2 (2018). http://dx.doi.org/10.1103/physreva.98.023627.

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31

Ganguly, Sudin, and Santanu K. Maiti. "Electrical analogue of one-dimensional and quasi-one-dimensional Aubry–André–Harper lattices." Scientific Reports 13, no. 1 (2023). http://dx.doi.org/10.1038/s41598-023-40690-9.

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AbstractThis work explores the potential for achieving correlated disorder in electrical circuits by utilizing reactive elements. By establishing a direct correspondence between the tight-binding Hamiltonian and the admittance matrix of the circuit, a novel approach is presented. The localization phenomena within the circuit are investigated through the analysis of the two-port impedance. To introduce correlated disorder, the Aubry–André–Harper (AAH) model is employed. Both one-dimensional and quasi-one-dimensional AAH structures are examined and effectively mapped to their tight-binding counterparts. Notably, transitions from a high-conducting phase to a low-conducting phase are observed in these circuits, highlighting the impact of correlated disorder.

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32

Cui, H. T., M. Qin, L. Tang, H. Z. Shen, and X. X. Yi. "Localization-enhanced dissipation in a generalized Aubry-André-Harper model coupled with Ohmic baths." Physics Letters A, July 2022, 128314. http://dx.doi.org/10.1016/j.physleta.2022.128314.

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33

Ahmed, Aamna, Nilanjan Roy, and Auditya Sharma. "Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model." Physical Review B 104, no. 15 (2021). http://dx.doi.org/10.1103/physrevb.104.155137.

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34

Cui, Hai-Tao, Ming Qin, Li Tang, Hongzhi Shen, and Xuexi Yi. "Localization-Enhanced Dissipation in a Generalized Aubry-André-Harper Model Coupled with Ohmic Baths." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4028998.

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35

Xu, Tong-Tong, and Jia-Rui Li. "Topological properties in Aubry-André-Harper model with p-wave superconducting pairing." Progress of Theoretical and Experimental Physics, April 11, 2023. http://dx.doi.org/10.1093/ptep/ptad043.

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Abstract We study the topological properties of the one-dimensional p-wave Aubry-André-Harper(AAH) model with periodic incommensurate potential and transition coupling. The calculation results show that due to co-influence of the incommensurate potential and modulation phase, three topological phases arise in different parameter regions: topologically-trivial phase, Su-Schrieffer-Heeger(SSH)-like topological phase, and Kitaev-like topological superconducting phase with Majorana zero modes. By evaluating the Andreev reflection conductance, we see that in the Kitaev-like phase, the quantized conductance plateau comes into being at the zero-bias limit, due to the occurrence of resonant Andreev reflection. In addition, when the disorder effect is incorporated, the SSH-like topology is modified sensitively and the degenerate topological states split, whereas the Kitaev-like topological phase is robust to weak disorder. Finally, we find that disorder can induce topological phase transition, i.e., from topologically-trivial phase to topological phase. Based on these results, we believe that our findings have significance for studying the topological phase transition in one-dimensional topological superconducting system. Also, it provides a feasible scheme for clarifying different topological phases.

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36

Li, Hao, Yong-Yi Wang, Yun-Hao Shi, et al. "Observation of critical phase transition in a generalized Aubry-André-Harper model with superconducting circuits." npj Quantum Information 9, no. 1 (2023). http://dx.doi.org/10.1038/s41534-023-00712-w.

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AbstractQuantum simulation enables study of many-body systems in non-equilibrium by mapping to a controllable quantum system, providing a powerful tool for computational intractable problems. Here, using a programmable quantum processor with a chain of 10 superconducting qubits interacted through tunable couplers, we simulate the one-dimensional generalized Aubry-André-Harper model for three different phases, i.e., extended, localized and critical phases. The properties of phase transitions and many-body dynamics are studied in the presence of quasi-periodic modulations for both off-diagonal hopping coefficients and on-site potentials of the model controlled respectively by adjusting strength of couplings and qubit frequencies. We observe the spin transport for initial single- and multi-excitation states in different phases, and characterize phase transitions by experimentally measuring dynamics of participation entropies. Our experimental results demonstrate that the recently developed tunable coupling architecture of superconducting processor extends greatly the simulation realms for a wide variety of Hamiltonians, and can be used to study various quantum and topological phenomena.

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37

Yoo, Yongchan, Junhyun Lee, and Brian Swingle. "Reply to “Comment on ‘Nonequilibrium steady state phases of the interacting Aubry-André-Harper model' ”." Physical Review B 103, no. 23 (2021). http://dx.doi.org/10.1103/physrevb.103.237102.

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38

Zeng, Qi-Bo, Shu Chen, and Rong Lü. "Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss." Physical Review A 95, no. 6 (2017). http://dx.doi.org/10.1103/physreva.95.062118.

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39

Tong, Xianqi, Ye-Ming Meng, Xunda Jiang, Chaohong Lee, Gentil Dias de Moraes Neto, and Gao Xianlong. "Dynamics of a quantum phase transition in the Aubry-André-Harper model with p -wave superconductivity." Physical Review B 103, no. 10 (2021). http://dx.doi.org/10.1103/physrevb.103.104202.

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40

Wang, B. X., and C. Y. Zhao. "Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model." Physical Review B 107, no. 12 (2023). http://dx.doi.org/10.1103/physrevb.107.125409.

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41

Roy, Nilanjan, and Auditya Sharma. "Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current." Physical Review B 100, no. 19 (2019). http://dx.doi.org/10.1103/physrevb.100.195143.

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42

Zhang, Dan-Wei, Yu-Lian Chen, Guo-Qing Zhang, Li-Jun Lang, Zhi Li, and Shi-Liang Zhu. "Skin superfluid, topological Mott insulators, and asymmetric dynamics in an interacting non-Hermitian Aubry-André-Harper model." Physical Review B 101, no. 23 (2020). http://dx.doi.org/10.1103/physrevb.101.235150.

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43

Zhao, X. L., Z. C. Shi, C. S. Yu, and X. X. Yi. "Effect of loss on the topological features of dimer chains described by the extended Aubry-André-Harper model." Physical Review A 95, no. 4 (2017). http://dx.doi.org/10.1103/physreva.95.043837.

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44

Cai, Xiaoming, and Shao-Jian Jiang. "Equivalence and superposition of real and imaginary quasiperiodicities." New Journal of Physics, October 13, 2022. http://dx.doi.org/10.1088/1367-2630/ac99f5.

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Abstract We take non-Hermitian Aubry-André-Harper models and quasiperiodic Kitaev chains as examples to demonstrate the equivalence and superposition of real and imaginary quasiperiodic potentials (QPs) on inducing localization of single-particle states. We prove this equivalence by analytically computing Lyapunov exponents (or inverse of localization lengths) for systems with purely real and purely imaginary QPs. Moreover, when superposed and with the same frequency, real and imaginary QPs are coherent on inducing the localization, in a way which is determined by the relative phase between them. The localization induced by a coherent superposition can be simulated by the Hermitian model with an effective strength of QP, implying that models are in the same universality class. When their frequencies are different and relatively incommensurate, they are incoherent and their superposition leads to less correlation effects. Numerical results show that the localization happens earlier and there is an intermediate mixed phase lacking of mobility edge.

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45

Fernández, Francisco M., Diego R. Alcoba, Alicia Torre, Luis Lain, Ofelia B. Oña, and Elias Ríos. "Comment on “Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current”." Physical Review B 101, no. 19 (2020). http://dx.doi.org/10.1103/physrevb.101.197101.

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46

Cai, Xiaoming, and YiCong Yu. "Exact mobility edges in quasiperiodic systems without self-duality." Journal of Physics: Condensed Matter, November 8, 2022. http://dx.doi.org/10.1088/1361-648x/aca136.

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Abstract Mobility edge (ME), a critical energy separating localized and extended states in spectrum, is a central concept in understanding localization physics. However, there are few models with exact MEs, and their presences are fragile against perturbations. In the paper, we generalize the Aubry-André-Harper model proposed in [Phys. Rev. Lett. 114, 146601 (2015)] and recently realized in [Phys. Rev. Lett. 126, 040603 (2021)], by introducing a relative phase in the quasiperiodic potential. Applying Avila’s global theory, we analytically compute localization lengths of all single-particle states and determine the exact expression of ME, which both signiﬁcantly depend on the relative phase. They are veriﬁed by numerical simulations, and physical perception of the exact expression is also provided. We show that old exact MEs, guaranteed by the delicate self-duality which is broken by the relative phase, are special ones in a series controlled by the phase. Furthermore, we demonstrate that out of expectation, exact MEs are invariant against a shift in the quasiperiodic potential, although the shift changes the spectrum and localization properties. Finally, we show that the exact ME is related to the one in the dual model which has long-range hoppings.

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47

Roy, Souvik, Sudin Ganguly, and Santanu K. Maiti. "Interplay between hopping dimerization and quasi-periodicity on flux-driven circular current in an incommensurate Su–Schrieffer–Heeger ring." Scientific Reports 13, no. 1 (2023). http://dx.doi.org/10.1038/s41598-023-31354-9.

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AbstractWe report for the first time the phenomenon of flux-driven circular current in an isolated Su–Schrieffer–Heeger (SSH) quantum ring in presence of cosine modulation in the form of the Aubry–André–Harper (AAH) model. The quantum ring is described within a tight-binding framework, where the effect of magnetic flux is incorporated through Peierls substitution. Depending on the arrangements of AAH site potentials we have two different kinds of ring systems that are referred to as staggered and non-staggered AAH SSH rings. The interplay between the hopping dimerization and quasiperiodic modulation leads to several new features in the energy band spectrum and persistent current which we investigate critically. An atypical enhancement of current with increasing AAH modulation strength is obtained that gives a clear signature of transition from a low conducting phase to a high conducting one. The specific roles of AAH phase, magnetic flux, electron filling, intra- and inter-cell hopping integrals, and ring size are discussed thoroughly. We also study the effect of random disorder on persistent current with hopping dimerization to compare the results with the uncorrelated ones. Our analysis can be extended further in studying magnetic responses of similar kinds of other hybrid systems in presence of magnetic flux.

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Yuan Tao, Dai Han-Ning, and Chen Yu-Ao. "Nonlinear Topological Pumping in Momentum Space Lattice of Ultracold atoms." Acta Physica Sinica, 2023, 0. http://dx.doi.org/10.7498/aps.72.20230740.

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Topological pumping enables the quantized transport of matter waves through an adiabatic evolution of the system, which plays an essential role in the applications of transferring quantum states and exploring the topological properties in higher-dimensional quantum systems. Recently, exploring the interplay between novel topological pumping and interactions has attracted growing attention in topological systems, such as nonlinear topological pumping induced by interactions. So far, the experimental realizations of the nonlinear topological pumps have been realized only in the optical waveguide systems with Kerr nonlinearity. It is still necessary to further explore the phenomenon in different systems. Here, we present an experimental proposal for realizing the nonlinear topological pumping via a one-dimensional (1D) off-diagonal Aubry-André-Harper (AAH) model with mean-field interactions in the momentum space lattice of ultracold atoms. In particular, we develop a numerical method for calculating the energy band of the nonlinear systems. With numerical calculations, we first solve the nonlinear energy band structure and soliton solution of the 1D nonlinear off-diagonal AAH model in the region of weak interaction strengths. The result shows that the lowest or the highest energy band is modulated in the nonlinear system of g>0 or g<0, respectively. The eigenstates of the associated energy bands have the features of the soliton solutions. We then show that the topological pumping of solitons exhibits quantized transport characteristics. Moreover, we numerically calculate the Chern number associated with the lowest and highest energy bands at different interaction strengths. The result shows that the quantized transport of solitons is determined by the Chern number of the associated energy band of the system from which solitons emanate. Finally, we propose a nonlinear topological pumping scheme based on a momentum lattice experimental system with <sup>7</sup>Li atoms. We can prepare the initial state, which is approximately the distribution of the soliton state of the lowest energy band, and calculate the dynamical evolution of this initial state in the case of U>0. Also, we analyzethe influence of adiabatic evolution conditions on the pumping process, demonstrating the feasibility of nonlinear topological pumping in the momentum lattice system. Our study provides a feasible route for investigating nonlinear topological pumping in ultracold atom systems, which is helpful for further exploring the topological transport in nonlinear systems, such as topological phase transitions and edge effects induced by nonlinearity.

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Zeng, Qi-Bo, Yan-Bin Yang, and Yong Xu. "Topological phases in non-Hermitian Aubry-André-Harper models." Physical Review B 101, no. 2 (2020). http://dx.doi.org/10.1103/physrevb.101.020201.

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Lin, Y. T., C. S. Weber, D. M. Kennes, M. Pletyukhov, H. Schoeller, and V. Meden. "Quantitative analysis of interaction effects in generalized Aubry-André-Harper models." Physical Review B 103, no. 19 (2021). http://dx.doi.org/10.1103/physrevb.103.195119.

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