Volume 25, Issue 3
Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models

Yueguang Shi & Warren E. Pickett

Commun. Comput. Phys., 25 (2019), pp. 651-668.

Published online: 2018-11

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  • Abstract

A lattice model of interacting fermions is studied with the principal aim of assessing the dependence of calculated mean-field ground states versus the N× N lattice size, with N = 16, 32, and 48. A two band model on the two-dimensional square lattice is simulated, with on-site energies and interaction parameters chosen to represent crystal field split orbitals in the moderately correlated regime. Nearest neighbor hopping leads to the well known van Hove singularities (vHs) of the square lattice. Anomalies in the inverse participation ratio of the eigenstates are found to be associated with the vHs, with their prevalence decreasing inversely with N. For the chosen model, inhomogeneous spin densities are always obtained for the small lattice size N=16, with the degree of variation decreasing rapidly for most polarizations as N is increased. Various spin polarizations are treated, and one case in which spin density inhomogeneity persists for the largest lattice size is discussed and analyzed. Coupling of spin density inhomogeneities to charge density variation is minor but evident, and is primarily of intra-orbital origin.

  • Keywords

Lattice Hamiltonian mean field lattice size moderate interactions.

  • AMS Subject Headings

71.10.Fd 71.15.Dx 75.30.Fv 75.10.Lp

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COPYRIGHT: © Global Science Press

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@Article{CiCP-25-651, author = {}, title = {Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {3}, pages = {651--668}, abstract = {

A lattice model of interacting fermions is studied with the principal aim of assessing the dependence of calculated mean-field ground states versus the N× N lattice size, with N = 16, 32, and 48. A two band model on the two-dimensional square lattice is simulated, with on-site energies and interaction parameters chosen to represent crystal field split orbitals in the moderately correlated regime. Nearest neighbor hopping leads to the well known van Hove singularities (vHs) of the square lattice. Anomalies in the inverse participation ratio of the eigenstates are found to be associated with the vHs, with their prevalence decreasing inversely with N. For the chosen model, inhomogeneous spin densities are always obtained for the small lattice size N=16, with the degree of variation decreasing rapidly for most polarizations as N is increased. Various spin polarizations are treated, and one case in which spin density inhomogeneity persists for the largest lattice size is discussed and analyzed. Coupling of spin density inhomogeneities to charge density variation is minor but evident, and is primarily of intra-orbital origin.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0089}, url = {http://global-sci.org/intro/article_detail/cicp/12824.html} }
TY - JOUR T1 - Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models JO - Communications in Computational Physics VL - 3 SP - 651 EP - 668 PY - 2018 DA - 2018/11 SN - 25 DO - http://dor.org/10.4208/cicp.OA-2018-0089 UR - https://global-sci.org/intro/cicp/12824.html KW - Lattice Hamiltonian KW - mean field KW - lattice size KW - moderate interactions. AB -

A lattice model of interacting fermions is studied with the principal aim of assessing the dependence of calculated mean-field ground states versus the N× N lattice size, with N = 16, 32, and 48. A two band model on the two-dimensional square lattice is simulated, with on-site energies and interaction parameters chosen to represent crystal field split orbitals in the moderately correlated regime. Nearest neighbor hopping leads to the well known van Hove singularities (vHs) of the square lattice. Anomalies in the inverse participation ratio of the eigenstates are found to be associated with the vHs, with their prevalence decreasing inversely with N. For the chosen model, inhomogeneous spin densities are always obtained for the small lattice size N=16, with the degree of variation decreasing rapidly for most polarizations as N is increased. Various spin polarizations are treated, and one case in which spin density inhomogeneity persists for the largest lattice size is discussed and analyzed. Coupling of spin density inhomogeneities to charge density variation is minor but evident, and is primarily of intra-orbital origin.

Yueguang Shi & Warren E. Pickett. (2020). Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models. Communications in Computational Physics. 25 (3). 651-668. doi:10.4208/cicp.OA-2018-0089
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