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Journal articles on the topic 'Fock lattice'

Author: Grafiati

Published: 6 September 2023

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1

YU, M., and H. Q. LIN. "PHASE SEPARATION IN THE TWO-DIMENSIONAL HUBBARD MODEL." International Journal of Modern Physics B 19, no. 01n03 (January 30, 2005): 299–302. http://dx.doi.org/10.1142/s021797920502844x.

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In this paper, we study phase separation in the two-dimensional single-band Hubbard model with the unrestricted Hartree-Fock(UHF) method and the restricted Hartree-Fock (RHF) method. We perform the calculation for square lattices and rectangle lattices. It is observed that the stripe phase exists and it depends on three aspects: geometry of the lattice, Coulomb interaction U and band filling n. To gain more physical insights, we consider the Hubbard model with spin dependent hoppings: t↑ and t↓, and study the effect of varying [Formula: see text] on the phase separation.

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2

Khoromskaia, Venera, and Boris N. Khoromskij. "Block Circulant and Toeplitz Structures in the Linearized Hartree–Fock Equation on Finite Lattices: Tensor Approach." Computational Methods in Applied Mathematics 17, no. 3 (July 1, 2017): 431–55. http://dx.doi.org/10.1515/cmam-2017-0004.

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AbstractThis paper introduces and analyzes the new grid-based tensor approach to approximate solutions of the elliptic eigenvalue problem for the 3D lattice-structured systems. We consider the linearized Hartree–Fock equation over a spatial{L_{1}\times L_{2}\times L_{3}}lattice for both periodic and non-periodic problem setting, discretized in the localized Gaussian-type orbitals basis. In the periodic case, the Galerkin system matrix obeys a three-level block-circulant structure that allows the FFT-based diagonalization, while for the finite extended systems in a box (Dirichlet boundary conditions) we arrive at the perturbed block-Toeplitz representation providing fast matrix-vector multiplication and low storage size. The proposed grid-based tensor techniques manifest the twofold benefits: (a) the entries of the Fock matrix are computed by 1D operations using low-rank tensors represented on a 3D grid, (b) in the periodic case the low-rank tensor structure in the diagonal blocks of the Fock matrix in the Fourier space reduces the conventional 3D FFT to the product of 1D FFTs. Lattice type systems in a box with Dirichlet boundary conditions are treated numerically by our previous tensor solver for single molecules, which makes possible calculations on rather large{L_{1}\times L_{2}\times L_{3}}lattices due to reduced numerical cost for 3D problems. The numerical simulations for both box-type and periodic{L\times 1\times 1}lattice chain in a 3D rectangular “tube” withLup to several hundred confirm the theoretical complexity bounds for the block-structured eigenvalue solvers in the limit of largeL.

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3

Welsh, Staszek, and David E. Logan. "Simple probability distributions on a Fock-space lattice." Journal of Physics: Condensed Matter 30, no. 40 (September 13, 2018): 405601. http://dx.doi.org/10.1088/1361-648x/aadd35.

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4

Gilmutdinov V. F., Timirgazin M. A., and Arzhnikov A. K. "Spiral magnetic order and metal-insulator transition in the Hubbard model on a triangular lattice." Physics of the Solid State 64, no. 1 (2022): 76. http://dx.doi.org/10.21883/pss.2022.01.52492.191.

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The magnetic phase diagrams of the two-dimensional Hubbard model forisotropic and anisotropic triangular lattices are constructed within theHartree--Fock and slave boson approximations. The triangular latticespecific non-collinear and spiral magnetic states, as well as phaseseparation between them, are shown to be realized in a wide range of modelparameters along with collinear magnetic states (stripe antiferromagneticand ferromagnetic). Phase transitions of the first and second order arefound, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree--Fock and slave boson, showsthat electronic correlations suppress magnetic states, the region ofparamagnetism being expand, for values U/t>~=5. At the same time, when theFermi level is near the van Hove singularity, electron correlations do notchange the diagrams qualitatively, which is consistent with the previouslyobtained result for square and cubic lattices. The results are comparedwith the data available in the literature for other methods and approaches. Keywords: Hubbard model, phase separation, spiral magnetic order, triangular lattice, metal-insulator transition\

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5

Qin, Mingpu. "Effect of hole doping on the 120 degree order in the triangular lattice Hubbard model: a Hartree–Fock revisit." Journal of Physics: Condensed Matter 34, no. 23 (April 5, 2022): 235603. http://dx.doi.org/10.1088/1361-648x/ac5e79.

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Abstract We revisit the unrestricted Hartree Fock study on the evolution of the ground state of the Hubbard model on the triangular lattice with hole doping. At half-filling, it is known that the ground state of the Hubbard model on triangular lattice develops a 120 degree coplanar order at half-filling in the strong interaction limit, i.e., in the spin 1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. The ground state property in the doped case is still in controversy even though extensive studies were performed in the past. Within Hartree Fock theory, we find that the 120 degree order persists from zero doping to about 0.3 hole doping. At 1/3 hole doping, a three-sublattice collinear order emerges in which the doped hole is concentrated on one of the three sublattices with antiferromagnetic Neel order on the remaining two sublattices, which forms a honeycomb lattice. Between the 120 degree order and 1/3 doping region, a phase separation occurs in which the 120 degree order coexists with the collinear anti-ferromagnetic order in different regions of the system. The collinear phase extends from 1/3 doping to about 0.41 doping, beyond which the ground state is paramagnetic with uniform electron density. The phase diagram from Hartree Fock could provide guidance for the future study of the doped Hubbard model on triangular lattice with more sophisticated many-body approaches.

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6

Oztas, Z. "Nondiffracting wave beams in non-Hermitian Glauber–Fock lattice." Physics Letters A 382, no. 17 (May 2018): 1190–93. http://dx.doi.org/10.1016/j.physleta.2018.02.037.

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7

Surratt, G. T., R. N. Euwema, and D. L. Wilhite. "HArtree-fock lattice constant and bulk modulus of diamond." International Journal of Quantum Chemistry 7, S7 (June 18, 2009): 607–11. http://dx.doi.org/10.1002/qua.560070770.

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8

Гильмутдинов, В. Ф., М. А. Тимиргазин, and А. К. Аржников. "Спиральное магнитное упорядочение и переход металл--диэлектрик в модели Хаббарда на треугольной решeтке." Физика твердого тела 64, no. 1 (2022): 79. http://dx.doi.org/10.21883/ftt.2022.01.51835.191.

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The magnetic phase diagrams of the two-dimensional Hubbard model for isotropic and anisotropic triangular lattices are constructed within the Hartree-Fock and slave boson approximations. The triangular lattice specific non-collinear and spiral magnetic states, as well as phase separation between them, are shown to be realized in a wide range of model parameters along with collinear magnetic states (stripe antiferromagnetic and ferromagnetic). Phase transitions of the first and second order are found, and the boundaries of the phase separation regions are determined. A comparison of the two approximations, Hartree-Fock and slave boson, shows that electronic correlations suppress magnetic states, the region of paramagnetism being expand, for values U/t>5. At the same time, when the Fermi level is near the van Hove singularity, electron correlations do not change the diagrams qualitatively, which is consistent with the previously obtained result for square and cubic lattices. The results are compared with the data available in the literature for other methods and approaches.

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9

Bendacha, M., and A. Boudjemâa. "Normal and anomalous densities in Bose–Einstein condensates with optical lattices." Canadian Journal of Physics 92, no. 5 (May 2014): 375–79. http://dx.doi.org/10.1139/cjp-2013-0396.

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We study the quantum phase transition from the superfluid to the Mott insulator state in two- and three-dimensional Bose–Einstein condensate with optical lattices using Bose–Hubbard Hamiltonian within the generalized Hatree–Fock–Bogoliubov approximation. The behavior of the depletion and the anomalous fraction has been investigated in the Mott insulator phase. We found that at T = 0, these quantities become significant in two and three dimensions. It is shown also that the dimensionality of the lattice enhances the anomalous density.

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10

Mandal, Saptarshi, and Sanjay Gupta. "Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field." Journal of Physics: Condensed Matter 34, no. 21 (March 29, 2022): 215602. http://dx.doi.org/10.1088/1361-648x/ac5d8a.

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Abstract We study the revival of Hofstadter butterfly due to the competition between disorder and electronic interaction using mean field approximation of unrestricted Hartree Fock method at zero temperature for two dimensional square and honeycomb lattices. Interplay of disorder and electronic correlation to nullify each other is corroborated by the fact that honeycomb lattice needs more strength of electronic correlation owing to its less co-ordination number which enhances the effect of disorder. The extent of revival of the butterfly is better in square lattice than honeycomb lattice due to higher coordination number. The effect of disorder and interaction is also investigated to study entanglement entropy and entanglement spectrum. We find that for honeycomb lattice area law of entanglement entropy is obeyed in all cases but for square lattice there is some departure from area law for larger subsystems. The entanglement spectrum have the reflection symmetry of the original butterfly of the Hofstadter spectrum. The interaction induces a gap in the entanglement spectrum as well conforming the correspondence between physical spectrum and entanglement spectrum. The effect of disorder closes the interaction induced gap in the entanglement spectrum establishing the nullification of interaction due to disorder and vice versa.

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11

KO, CHUL KI, and HYUN JAE YOO. "INTERACTING FOCK SPACES AND THE MOMENTS OF THE LIMIT DISTRIBUTIONS FOR QUANTUM RANDOM WALKS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 01 (March 2013): 1350003. http://dx.doi.org/10.1142/s0219025713500033.

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We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.

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12

Tulkin, Tulkin, and Shokhida Nematova. "INVESTIGATION OF THE SPECTRUM OF A GENERALIZED FRIEDRICHS MODEL: NON-INTEGRAL LATTICE CASE." Scientific Reports of Bukhara State University 3, no. 1 (January 30, 2019): 5–11. http://dx.doi.org/10.52297/2181-1466/2019/3/1/1.

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The article investigates the essential and discrete spectrum of the self-adjoint generalized Friedrichs model. This model corresponds to a system consisting of no more than two particles on a non-integral lattice, and operates in a truncated subspace of Fock space. The number and location of eigenvalues is determined according to the "interaction parameter". Anobvious form of the eigenvectors is found

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13

Marinelli, F., M. Roche, I. Baraille, and C. Pouchan. "Lattice dynamics of magnesium using pseudopotential andab initioHartree-Fock approaches." Physical Review B 54, no. 9 (September 1, 1996): 6054–57. http://dx.doi.org/10.1103/physrevb.54.6054.

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14

Hamber, Herbert W., and Lu Heng Sunny Yu. "Dyson’s Equations for Quantum Gravity in the Hartree–Fock Approximation." Symmetry 13, no. 1 (January 12, 2021): 120. http://dx.doi.org/10.3390/sym13010120.

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Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge–Wheeler lattice path integral lends itself well for that purpose. Nevertheless, lattice methods ultimately rely on extensive numerical calculations, leaving a desire for alternate methods that can be pursued analytically. In this work, we outline the Hartree–Fock approximation to quantum gravity, along lines which are analogous to what is done for scalar fields and gauge theories. The starting point is Dyson’s equations, a closed set of integral equations which relate various physical amplitudes involving graviton propagators, vertex functions, and proper self-energies. Such equations are in general difficult to solve, and as a result they are not very useful in practice, but nevertheless provide a basis for subsequent approximations. This is where the Hartree–Fock approximation comes in, whereby lowest order diagrams get partially dressed by the use of fully interacting Green’s function and self-energies, which then lead to a set of self-consistent integral equations. The resulting nonlinear equations for the graviton self-energy show some remarkable features that clearly distinguish it from the scalar and gauge theory cases. Specifically, for quantum gravity one finds a nontrivial ultraviolet fixed point in Newton’s constant G for spacetime dimensions greater than two, and nontrivial scaling dimensions between d=2 and d=4, above which one obtains Gaussian exponents. In addition, the Hartree–Fock approximation gives an explicit analytic expression for the renormalization group running of Newton’s constant, suggesting gravitational antiscreening with Newton’s constant slowly increasing on cosmological scales.

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15

Kunz, A. Barry, and John M. Vail. "Quantum-mechanical cluster-lattice interaction in crystal simulation: Hartree-Fock method." Physical Review B 38, no. 2 (July 15, 1988): 1058–63. http://dx.doi.org/10.1103/physrevb.38.1058.

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16

Kim, B., M. H. Chung, and J. H. Kwon. "Decomposition of the Fock Space in Two-Dimensional Square Lattice Systems." Letters in Mathematical Physics 78, no. 1 (September 6, 2006): 73–88. http://dx.doi.org/10.1007/s11005-006-0104-4.

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17

CELEGHINI, E., S. DE MARTINO, S. DE SIENA, G. VITIELLO, and M. RASETTI. "QUANTUM GROUPS, SQUEEZING, BLOCH, AND THETA FUNCTIONS." Modern Physics Letters B 07, no. 20 (August 30, 1993): 1321–29. http://dx.doi.org/10.1142/s0217984993001363.

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We realize the deformation of the Weyl–Heisenberg algebra in terms of finite difference operators within the Fock–Bargmann representation. This allows us to incorporate in a unified q-algebra structure, the notions of squeezing and lattice quantum systems resorting to the properties of theta functions.

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18

Costa, N. C., J. P. Lima, and Raimundo R. dos Santos. "Spiral magnetic phases on the Kondo Lattice Model: A Hartree–Fock approach." Journal of Magnetism and Magnetic Materials 423 (February 2017): 74–83. http://dx.doi.org/10.1016/j.jmmm.2016.09.061.

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19

LITAK, GRZEGORZ, and TADEUSZ DOMAŃSKI. "SUPERCONDUCTIVITY WITH ‘η PAIRING’: GAP PARAMETER AND SINGLE PARTICLE TUNNELING." Modern Physics Letters B 08, no. 03 (February 10, 1994): 149–57. http://dx.doi.org/10.1142/s0217984994000169.

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We examine the ‘η pairing’ superconductivity using the negative U Hubbard model on the bipartite lattice. The superconducting gap parameter for η pairing is compared with the equilibrium Hartree-Fock-Bogolubov solution for the half-filled system in various temperatures and strengths of interaction. The quasiparticle density of states and the single particle tunneling are investigated.

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20

MAEDA, NOBUKI. "ANISOTROPY IN THE COMPRESSIBLE QUANTUM HALL STATE." International Journal of Modern Physics B 15, no. 10n11 (May 10, 2001): 1373–76. http://dx.doi.org/10.1142/s0217979201005854.

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Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around ν=l+1/2 in the quantum Hall system. The Hartree-Fock energy of the unidirectional charge density wave (UCDW) are calculated self-consistently. In these states the UCDW seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermion systems which extend to the uniform direction. The kinetic energy of this one-dimensional system is induced from the Coulomb interaction term and the self-consistent Fermi surface is obtained.

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21

Palmer, Michael H. "Quadrupole Coupling in Purines and Pyrimidines by Hartree-Fock Lattice Calculations of Electric Field Gradients." Zeitschrift für Naturforschung A 51, no. 5-6 (June 1, 1996): 479–88. http://dx.doi.org/10.1515/zna-1996-5-623.

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Abstract We present ab initio Hartree-Fock lattice calculations on adenine, guanine and hypoxanthine, and some pyrimidines, including cytosine and uracil derivatives. The electric field gradients at the nitrogen centres are related to NQR experimental determinations of nuclear quadrupole coupling constants. The calculations were performed as lattice calculations in the unit cell environment, with 6-31G or double zeta basis sets at the SCF level. The present analysis strongly suggests that χzz at N3 in cytosine, N3 in guanine are both positive, and approximately tangential to the ring at that centre. In contrast, N7 in guanine is like most other azine-type N centres, with a largely radial direction for χzz. The 3-protonated cytosine ring has χzz as the local π-direction.

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22

Palmer, Michael H., and John A. Blair-Fish. "Quadrupole Coupling in some H-bonded Organic Systems by ab initio Lattice Calculations of Electric Field Gradients." Zeitschrift für Naturforschung A 49, no. 1-2 (February 1, 1994): 146–54. http://dx.doi.org/10.1515/zna-1994-1-223.

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Abstract We present ab initio Hartree-Fock lattice calculations performed in the unit cell environment, to compute a wave-function and the derived electric field gradients for the bulk material. These calculations differ from cluster calculations by including the effects of more distant neighbour molecules. Examples considered are ammonia, formamide, oxamide, urea, thiourea, uracil, para-banic acid, alloxan, guanidine bicarbonate and melamine.

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23

ISHIKAWA, K., T. AOYAMA, Y. ISHIZUKA, and N. MAEDA. "FIELD THEORY OF ANISOTROPIC QUANTUM HALL GAS: METROLOGY AND A NOVEL QUANTUM HALL REGIME." International Journal of Modern Physics B 17, no. 27 (October 30, 2003): 4765–818. http://dx.doi.org/10.1142/s0217979203023112.

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The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the Hall conductance is derived and is used for the proof of the integer quantum Hall effect in the realistic situation. Anisotropic quantum Hall gas is investigated based on the Hartree–Fock approximation in the same formalism. Thermodynamic properties, transport properties, and unusual response under external modulations are found. Implications for the integer quantum Hall effect in the finite systems are also studied and a new quantum Hall regime with non-zero longitudinal resistance is shown to exist.

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24

FERTIG, H. A. "SKYRMIONS IN QUANTUM HALL FERROMAGNETS." International Journal of Modern Physics B 13, no. 05n06 (March 10, 1999): 461–68. http://dx.doi.org/10.1142/s0217979299000357.

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Properties of skyrmions in quantum Hall systems are reviewed. It is shown that, using a Hartree-Fock technique, the size of skyrmions near filling factor ν=1 may be computed, yielding a result in close agreement with experiment. Finite densities of skyrmions are shown to lead to a crystal state with square symmetry due to the spin-dependent nature of their mutual interactions. The square lattice state has an unusual spin ordering which leads to a new gapless mode, analogous to spin waves in a two-dimensional XY antiferromagnet. The stability of the ordered spin state is assessed using a time-dependent Hartree-Fock approach, and a phase diagram is derived which shows the parameter range for which long-range spin ordering is destroyed by quantum fluctuations.

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25

Fabbri, Marc A., and Frank Okoh. "Representations of Virasoro-Heisenberg Algebras and Virasoro-Toroidal Algebras." Canadian Journal of Mathematics 51, no. 3 (June 1, 1999): 523–45. http://dx.doi.org/10.4153/cjm-1999-024-x.

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AbstractVirasoro-toroidal algebras, , are semi-direct products of toroidal algebras and the Virasoro algebra. The toroidal algebras are, in turn, multi-loop versions of affine Kac-Moody algebras. Let Γ be an extension of a simply laced lattice by a hyperbolic lattice of rank two. There is a Fock space V(Γ) corresponding to Γ with a decomposition as a complex vector space: V(Γ) = . Fabbri and Moody have shown that when m ≠ 0, K(m) is an irreducible representation of . In this paper we produce a filtration of -submodules of K(0). When L is an arbitrary geometric lattice and n is a positive integer, we construct a Virasoro-Heisenberg algebra . Let Q be an extension of by a degenerate rank one lattice. We determine the components of V(Γ) that are irreducible -modules and we show that the reducible components have a filtration of -submodules with completely reducible quotients. Analogous results are obtained for . These results complement and extend results of Fabbri and Moody.

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26

Kim, B., and M. H. Chung. "Decomposition of the Fock space in two-dimensional triangle and honeycomb lattice systems." European Physical Journal B 60, no. 1 (November 2007): 67–73. http://dx.doi.org/10.1140/epjb/e2007-00328-7.

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27

Catti, M., A. Pavese, R. Dovesi, and V. R. Saunders. "Static lattice and electron properties ofMgCO3(magnesite) calculated byab initioperiodic Hartree-Fock methods." Physical Review B 47, no. 15 (April 15, 1993): 9189–98. http://dx.doi.org/10.1103/physrevb.47.9189.

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28

Igoshev, Peter A., Timofey V. Antipin, and Valentin Yu Irkhin. "Spiral Magnetism and Non-Uniform States in the Anderson Lattice Model." Materials Science Forum 845 (March 2016): 117–21. http://dx.doi.org/10.4028/www.scientific.net/msf.845.117.

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The ground-state magnetic phase diagram is calculated within the two-dimensional Anderson lattice model by employing a generalized Hartree-Fock approximation for the spiral magnetic ordering, as well as collinear one. The first-order transitions between different types of magnetic order are treated consistently, which allows one to describe the ''magnetic" phase separation. The features of magnetic order for the cases of integer and intermediate valence turn out to be substantially different. In the corresponding particular cases, the results are in a qualitative agreement with those for the s-d exchange and Hubbard models.

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29

El-Badry, Azza, Shemi Soliman, and Mahmoud Salah. "Hartree-Fock Approach for Rotating Bose-Einstein Condensation in One-dimensional Deep Optical Lattice." Egyptian Journal of Physics 45, no. 1 (In Progress) (November 1, 2017): 1–9. http://dx.doi.org/10.21608/ejphysics.2017.4256.

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30

Tomita, Norikazu, Shuji Watanabe, Keisuke Shida, H. Gomi, and A. Takahashi. "Visualization of quantum electronic and lattice fluctuations by using the resonating Hartree-Fock method." Journal of Physics: Conference Series 410 (February 8, 2013): 012159. http://dx.doi.org/10.1088/1742-6596/410/1/012159.

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31

Mizokawa, T., and A. Fujimori. "Self-energy correction to unrestricted Hartree-Fock solutions of lattice models for3dtransition-metal oxides." Physical Review B 53, no. 8 (February 15, 1996): R4201—R4204. http://dx.doi.org/10.1103/physrevb.53.r4201.

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32

Yamashiro, A., A. Ikawa, and H. Fukutome. "Hartree-Fock calculations for the electronic and lattice structures in heavily sodium doped polyacetylene." Synthetic Metals 85, no. 1-3 (March 1997): 1061–64. http://dx.doi.org/10.1016/s0379-6779(97)80150-6.

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33

Mendel, E., and L. Polley. "Negative-energy spinors and the Fock space of lattice fermions at finite chemical potential." Zeitschrift für Physik C Particles and Fields 65, no. 1 (March 1995): 127–34. http://dx.doi.org/10.1007/bf01571313.

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Aza, N. J. B., L. C. P. A. M. Müssnich, and A. F. Reyes-Lega. "A Z2-topological index as a Z2-state index." Journal of Mathematical Physics 63, no. 6 (June 1, 2022): 061901. http://dx.doi.org/10.1063/5.0089779.

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Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in the [Formula: see text] lattice, we depart from the well-known Araki–Evans [Formula: see text] index for quasi-free fermion states and rewrite it in terms of states rather than in terms of basis projections. Furthermore, we reformulate results that relate equivalences of Fock representations to the index parity into results that relate equivalences of Gel’fand–Naimark–Segal representations and the associated index parity.

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35

Zhuravlev, Yurii N., and Victor V. Atuchin. "Investigation of the Optical Spectra of Barium-Zinc (Aluminum) Fluoroborates and Barium-Zinc Fluorocarbonate from First Principles." Symmetry 15, no. 8 (July 28, 2023): 1504. http://dx.doi.org/10.3390/sym15081504.

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The Raman scattering, infrared absorption, and reflection spectra of hexagonal non-centrosymmetric BaZnBO3F and BaAlBO3F2 and centrosymmetric BaZn3BO3F2 and BaZnCO3F2 are calculated using the standard procedures of the CRYSTAL package with the basis of localized orbitals and the B3LYP hybrid functional within the framework of the Hartree-Fock conjugate perturbation method. It is shown that the layered structure of crystals manifests itself in the spectra of vibrational modes polarized along and perpendicular to the c axis with wavenumbers for the lattice region formed by displacements of atoms in [BaF]∞ and [MAO3]∞ (M: Zn, Al; A: B, C) layers, for molecular deformation outside and in the plane of anions BO3 and CO3. The quantitative and qualitative composition of the spectra is determined by the symmetry of the crystal lattice.

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36

Palmer, Michael H. "Nuclear Quadrupole Coupling Constant assignments for a series of azoles and azines by Hartree-Fock SCF-Cluster and Lattice Calculations." Zeitschrift für Naturforschung A 51, no. 5-6 (June 1, 1996): 451–59. http://dx.doi.org/10.1515/zna-1996-5-621.

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Abstract We present ab initio Hartree-Fock lattice calculations on a series of heterocyclic and other compounds. Some of these have previously been studied by cluster calculations with the same DZ basis sets at the SCF level. The electric field gradients at the nitrogen centres, are related to NQR experimental determinations of nuclear quadrupole coupling constants. The compounds studied include imidazole and pyrazole, 4-nitroimidazole, 4-nitropyrazole, pyrazine, and tetramethylpyrazine, pyridinium chloride, and N-methylpyridinium iodide, and pyridine-N-oxide.

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37

BARLAS, YAFIS, WEI-CHENG LEE, KENTATO NOMURA, and ALLAN H. MACDONALD. "RENORMALIZED LANDAU LEVELS AND PARTICLE-HOLE SYMMETRY IN GRAPHENE." International Journal of Modern Physics B 23, no. 12n13 (May 20, 2009): 2634–40. http://dx.doi.org/10.1142/s0217979209062104.

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In this proceedings paper we report on a calculation of graphene's Landau levels in a magnetic field. Our calculations are based on a self-consistent Hartree-Fock approximation for graphene's massless-Dirac continuum model. We find that because of graphene's chiral band structure interactions not only shift Landau-level energies, as in a non-relativistic electron gas, but also alter Landau level wavefunctions. We comment on the subtle continuum model regularization procedure necessary to correctly maintain the lattice-model's particle hole symmetry properties.

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38

Sinayskiy, Ilya, and Francesco Petruccione. "Quantum optical implementation of open quantum walks." International Journal of Quantum Information 12, no. 02 (March 2014): 1461010. http://dx.doi.org/10.1142/s0219749914610103.

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A quantum optical implementation of the recently proposed open quantum walks (OQWs) is suggested. In the presented quantum optical scheme a two level atom plays the role of the "walker" and the Fock states of the cavity mode correspond to the lattice sites of the OQW. Using the small unitary rotations approach the effective dynamics of the system is shown to be an OQW. The presented scheme allows for a simple physical implementation of the OQW formalism, but it can be extended to create more diverse OQWs.

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39

Eglitis, R. I., R. I. Eglitis, A. V. Postnikov, and G. Borstel. "Semi-Empirical Hartree-Fock Simulations of Lattice Relaxation and Effective Interactions in Li-Doped KTaO3." physica status solidi (b) 209, no. 1 (September 1998): 187–93. http://dx.doi.org/10.1002/(sici)1521-3951(199809)209:1<187::aid-pssb187>3.0.co;2-4.

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40

Чернышев, В. А., and В. С. Рюмшин. "Cтруктура и динамика решетки кристаллов Nd-=SUB=-2-=/SUB=-TiO-=SUB=-5-=/SUB=- и Sm-=SUB=-2-=/SUB=-TiO-=SUB=-5-=/SUB=-: ab initio расчет." Физика твердого тела 61, no. 6 (2019): 1151. http://dx.doi.org/10.21883/ftt.2019.06.47693.337.

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Crystal structure and phonon spectra R2TiO5 (R = Nd, Sm) were studied within the framework of density functional theory and MO LKAO approach. The calculations were performed by using hybrid functional that takes into account both local and nonlocal (at the Hartree-Fock formalism) exchange. The coordinates of the ions in the unit cell and the lattice constants are calculated. The fundamental vibration frequencies of R2TiO5 (R = Nd, Sm) were calculated. The relative intensities of the Raman lines and the intensity of the IR-active modes have been calculated. The elastic constants of the crystal have been calculated at the first time.

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41

Ayuela, A., J. M. Lopez, J. A. Alonso, and V. Lua na. "Article." Canadian Journal of Physics 76, no. 4 (April 1, 1998): 311–20. http://dx.doi.org/10.1139/p98-003.

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(NaCl)nNa+ clusters whit n up to 15 have been studied using the ab initio Perturbed-Ion model, which is based on the Hartree--Fock method and the Theory of Electronic Separability. The energetics and structural properties are discussed in detail in the size range n <=10. Even for those small sizes, a certain tendency to form fragments of the rock-salt lattice is evident, although the excess repulsion of the cations induces distortions. We have also studied the addition and the removal of one or two NaCl molecules to (or from) (NaCl)13Na+.PACS Nos. 31.20Gm and 36.40+d

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42

Maruyama, Takaaki, Fumikazu Sato, and Norikazu Tomita. "Resonating Hartree-Fock studies on magnetic states in the Hubbard model on the uniform triangular lattice." Journal of Physics: Conference Series 320 (September 28, 2011): 012061. http://dx.doi.org/10.1088/1742-6596/320/1/012061.

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43

Mizokawa, T., and A. Fujimori. "Unrestricted Hartree-Fock study of transition-metal oxides: Spin and orbital ordering in perovskite-type lattice." Physical Review B 51, no. 18 (May 1, 1995): 12880–83. http://dx.doi.org/10.1103/physrevb.51.12880.

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44

Dovesi, R., R. Orlando, F. Ricca, and C. Roetti. "Co adsoprtion on MgO crystals: Hartree-fock calculations for regular adlayers on a (001) lattice plane." Surface Science 186, no. 1-2 (July 1987): 267–78. http://dx.doi.org/10.1016/s0039-6028(87)80048-1.

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45

Dovesi, R., R. Orlando, F. Ricca, and C. Roetti. "CO adsorption on MgO crystals: Hartree-fock calculations for regular adlayers on a (001) lattice plane." Surface Science Letters 186, no. 1-2 (July 1987): A285. http://dx.doi.org/10.1016/0167-2584(87)90626-8.

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46

Dovesi, R., R. Orlando, F. Ricca, and C. Roetti. "CO adsorption on MgO crystals: Hartree-Fock calculations for regular adlayers on a (001) lattice plane." Surface Science Letters 186, no. 3 (August 1987): 285. http://dx.doi.org/10.1016/0167-2584(87)91272-2.

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47

Ikawa, A., and M. Ozaki. "Group theoretical classification of the Hartree-Fock solutions of the Hubbard model on a triangular lattice." Journal of Physics: Condensed Matter 4, no. 15 (April 13, 1992): 4039–46. http://dx.doi.org/10.1088/0953-8984/4/15/016.

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48

CABO MONTES DE OCA, A., N. H. MARCH, and A. CABO-BIZET. "HARTREE–FOCK SOLUTIONS OF 2D INTERACTING TIGHT-BINDING ELECTRONS: MOTT PROPERTIES AND ROOM TEMPERATURE SUPERCONDUCTIVITY INDICATIONS." International Journal of Modern Physics B 28, no. 04 (January 22, 2014): 1450027. http://dx.doi.org/10.1142/s0217979214500271.

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Former results for a tight-binding (TB) model of CuO planes in La 2 CuO 4 are reinterpreted here to underline their wider implications. It is noted that physical systems being appropriately described by the TB model can exhibit the main strongly correlated electron system (SCES) properties, when they are solved in the HF approximation, by also allowing crystal symmetry breaking effects and noncollinear spin orientations of the HF orbitals. It is argued how a simple 2D square lattice system of Coulomb interacting electrons can exhibit insulator gaps and pseudogap states, and quantum phase transitions as illustrated by the mentioned former works. A discussion is also presented here indicating the possibility of attaining room temperature superconductivity, by means of a surface coating with water molecules of cleaved planes of graphite, being orthogonal to its c-axis. The possibility that 2D arrays of quantum dots can give rise to the same effect is also proposed to consideration. The analysis also furnishes theoretical insight to solve the Mott–Slater debate, at least for the La 2 CuO 4 and TMO band structures. The idea is to apply a properly noncollinear GW scheme to the electronic structure calculation of these materials. The fact is that the GW approach can be viewed as a HF procedure in which the screening polarization is also determined. This directly indicates the possibility of predicting the assumed dielectric constant in the previous works. Thus, the results seem to identify that the main correlation properties in these materials are determined by screening. Finally, the conclusions also seem to be of help for the description of the experimental observations of metal-insulator transitions and Mott properties in atoms trapped in planar photonic lattices.

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Göbel, K., and F. Wahl. "Electron Density Distribution of a Single Hydrogen Perturbation in a Metal Lattice." Zeitschrift für Naturforschung A 42, no. 5 (May 1, 1987): 431–37. http://dx.doi.org/10.1515/zna-1987-0501.

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The electronic structure of hydrogen centres stored in a metal crystal is described by a microscopic theory based on a functional energy difference method. That formalism works in a suitably chosen tensor product space built on a physical quasi-particle vacuum state. A transformation back to a bare Fock space representation is shown. This transformation operator divides the functional eigenvalue equation into a difference of two Schrödinger problems. The resulting state vectors can be used to calculate the electronic density distribution of a hydrogen excess electron in a metal lattice. The density function is obtained in a higher order approximation which considers the influence of three-particle correlations. A numerical solution is discussed for the case of a single hydrogen centre in a magnesium crystal. The plot shows that the excess electron is mainly localized in the surroundings of the corresponding hydrogen core. But with increasing host lattice extension there is more and more a non-vanishing probability to find the hydrogen electron dipped into the Fermi sea of metal electrons.

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50

Ghassemi Tabrizi, Shadan, and Carlos A. Jiménez-Hoyos. "Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach." Condensed Matter 8, no. 1 (February 3, 2023): 18. http://dx.doi.org/10.3390/condmat8010018.

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Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree–Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site–spin product state for the restoration of spin- and point-group symmetry, cPHF groups sites into discrete clusters and uses a cluster-product state as the broken-symmetry reference. Intracluster correlation is thus already included at the mean-field level, and intercluster correlation is introduced through symmetry projection. Variants of cPHF differing in the broken and restored symmetries are evaluated for ground states and singlet-triplet gaps of antiferromagnetic spin rings for various cluster sizes, where cPHF in general affords a significant improvement over ordinary PHF, although the division into clusters lowers the cyclical symmetry. In contrast, certain two- or three-dimensional spin arrangements permit cluster groupings compatible with the full spatial symmetry. We accordingly demonstrate that cPHF yields approximate ground states with correct spin- and point-group quantum numbers for honeycomb lattice fragments and symmetric polyhedra.

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