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arXiv:0912.4155 · Acta Physica Polonica A

The Falicov-Kimball Model in External Magnetic Field: Orbital Effects

M. Wróbel, Marcin Mierzejewski, Maciej M. Maśka

Published Aug 1, 2010• 7 citations
arXivHTMLPDF

Abstract

We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice.The field is taken into account by the Peierls substitution in the hopping term.We show how the Hofstadter butterfly is affected by electronic correlations.In the non-interacting case the field dependent energy spectrum forms the famous Hofstadter butterfly.Our results indicate that for arbitrary nonzero interaction strength and arbitrary magnetic field there is a gap in the energy spectrum at sufficiently low temperature.The gap vanishes with increase of temperature for weak coupling, however, it persists at high temperatures if the coupling is strong enough.Numerical results have been obtained with the help of Monte Carlo technique based on a modified Metropolis algorithm.

DOI
10.12693/aphyspola.118.379

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Journal of Physics Conference Series•Jan 1, 2010•1 citation
We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice.The field is taken into account by the Peierls substitution in the hopping term.We show how the Hofstadter butterfly is affected by electronic correlations.In the non-interacting case the field dependent energy spectrum forms the famous Hofstadter butterfly.Our results indicate that for arbitrary nonzero interaction strength and arbitrary magnetic field there is a gap in the energy spectrum at sufficiently low temperature.The gap vanishes with increase of temperature for weak coupling, however, it persists at high temperatures if the coupling is strong enough.Numerical results have been obtained with the help of Monte Carlo technique based on a modified Metropolis algorithm.
We investigate a finite two-dimensional system in the presence of an external magnetic field. We discuss how the energy spectrum depends on the system size, boundary conditions, and Coulomb repulsion. On one hand, using these results, we present the field dependence of the transport properties of a nanosystem. In particular, we demonstrate that these properties depend on whether the system consists of an even or an odd number of sites. On the other hand, on the basis of exact results obtained for a finite system, we investigate whether the Hofstadter butterfly is robust against strong electronic correlations. We show that for sufficiently strong Coulomb repulsion, the Hubbard gap decreases when the magnetic field increases.
Abstract The Hofstadter–Hubbard model captures the physics of strongly correlated electrons in an applied magnetic field, which is relevant to many recent experiments on Moiré materials. Few large-scale, numerically exact simulations exists for this model. In this work, we simulate the Hubbard–Hofstadter model using the determinant quantum Monte Carlo (DQMC) algorithm. We report the field and Hubbard interaction strength dependence of charge compressibility, fermion sign, local moment, magnetic structure factor, and specific heat. The gross structure of magnetic Bloch bands and band gaps determined by the non-interacting Hofstadter spectrum is preserved in the presence of U. Incompressible regions of the phase diagram have improved fermion sign. At half filling and intermediate and larger couplings, a strong orbital magnetic field delocalizes electrons and reduces the effect of Hubbard U on thermodynamic properties of the system.
Combined effects of correlated electron hopping, electron correlations and orbital magnetic field are studied on ground state properties of spinless Falicov-Kimball model (FKM). Results are obtained for finite size triangular lattice with periodic boundary conditions using numerical diagonalization and Monte-Carlo simulation techniques. It is found that the ground state configurations of electrons strongly depend on correlated electron hopping, onsite Coulomb interaction and orbital magnetic field. Several interesting configurations e.g. regular, segregated, axial and diagonal striped and hexagonal phases are found with change in correlated hopping and magnetic field. Study of density of states reveals that magnetic field induces a metal to insulator transition accompanied by segregated phase to an ordered phase. These results are applicable to the systems of recent interest like GdI2, NaTiO2 and MgV2O4 and can also be seen experimentally in cold atomic set up.
The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
The finite-temperature properties of the three-dimensional Falicov-Kimball model are studied in the symmetric case using the classical Monte-Carlo method. Analysing the temperature dependence of the specific heat C V,N we have found that the system exhibits the phase transition from the low-temperature ordered phase to the high-temperature disordered phase. The critical temperature of the phase transition is calculated numerically from the position of the maximum of C V,N and it is shown that its value in the three-dimensional case is considerably enhanced in comparison to the two-dimensional case. In addition, the temperature dependence of the itinerant electron density of states (DOS) is analysed. For very low-temperatures we have observed a formation of fine structure inside the principal gap that transforms to a pseudo-gap at higher temperatures and becomes temperature independent for sufficiently large temperatures. In this temperature region we have calculated DOS for different Coulomb interactions and found the Mott-Hubbard metal-insulator transition.