Robustness of the topological quantization of the Hall conductivity for correlated lattice electrons at finite temperatures

Abstract

Electrons on a two-dimensional (2d) lattice which is exposed to a strong uniform magnetic field show intriguing physical phenomena. The spectrum of such systems exhibits a complex (multi-)band structure known as Hofstadter's butterfly. For fillings at which the system is a band insulator one observes a quantized integer-valued Hall conductivity σxy corresponding to a topological invariant, the first Chern number C1. This is robust against many-body interactions as long as no changes in the gap structure occur. Strictly speaking, this stability holds only at zero temperatures T while for T > 0 correlation effects have to be taken into account. In this work, we address this question by presenting a dynamical mean field theory (DMFT) study of the Hubbard model in a uniform magnetic field. The inclusion of local correlations at finite temperature leads to (i) a shrinking of the integer plateaus of σxy as a function of the chemical potential and (ii) eventually to a deviation from these integer values. We demonstrate that these effects can be related to a correlation-driven narrowing and filling of the band gap, respectively. arXiv:1904.05087v1 [cond-mat.str-el]

Interacting Chern Insulator in Infinite Spatial Dimensions

“…Condition (28) is obtained as follows: We use Σ(ω) = a + (1 − z −1 )ω + O(ω 2 ) in Dyson's equation to get the "coherent" Green's function…”

“…Our answer is affirmative. Assuming locality of the self-energy, previous DMFT studies of correlated topological insulators have addressed two-dimensional systems, such as the Haldane model [27], Hofstadter's butterfly [28], or the BHZ model [29,30], all supplemented by interaction terms, or real three-dimensional systems, such as SmB 6 [31], combining the DMFT with ab initio band theory. A DMFT study of an interacting, topologically nontrivial model on a D = ∞ lattice is still missing.…”

Local vs non-local correlation effects in interacting quantum spin Hall insulators

“…To diagnose the topological properties of interacting systems, various schemes based on effective Hamiltonians as well as on Green's functions [54][55][56] have been formulated. Here, we make use of the well-established topological Hamiltonian [57], defined as…”

Thermodynamics of correlated electrons in a magnetic field

“…In the literature, this is sometimes called the Hofstadter-Hubbard or Hubbard-Hofstadter model. This model has been investigated using Hartree-Fock mean-field theory [21,22], exact diagonalization [23,24], dynamical mean-field theory [25,26], and in the large U limit via renormalized mean-field theory [27]. Aside from exact diagonalization, which is limited to small system sizes, all methods used to study the Hubbard-Hofstadter model have been approximate and don't capture the full extent of quantum fluctuations.…”

“…Aside from exact diagonalization, which is limited to small system sizes, all methods used to study the Hubbard-Hofstadter model have been approximate and don't capture the full extent of quantum fluctuations. It is not conclusive, for example, whether interactions change or preserve the gap structure of the Hofstadter butterfly [22,24,26].…”