Interaction-induced topological and magnetic phases in the Hofstadter-Hubbard model

Abstract

Interaction effects have been a subject of contemporary interest in topological phases of matter. But in the presence of interactions, the accurate determination of topological invariants in their general form is difficult due to their dependence on multiple integrals containing Green's functions and their derivatives. Here we employ the recently proposed "effective topological Hamiltonian" approach to explore interaction-induced topological phases in the time-reversal-invariant Hofstadter-Hubbard model. Within this approach, the zero-frequency part of the self-energy is sufficient to determine the correct topological invariant. We combine the topological Hamiltonian approach with the local self-energy approximation, both for the static and the full dynamical self-energy evaluated using dynamical mean field theory (DMFT), and present the resulting phase diagram in the presence of many-body interactions. We investigate the emergence of quantum spin Hall (QSH) states for different interaction strengths by calculating the Z2 invariant. The interplay of strong correlations and a staggered potential also induces magnetic long-range order with an associated first order transition. We present results for the staggered magnetisation (ms), staggered occupancy (ns) and double occupancy across the transition.PACS numbers: topological Hamiltonian, cold atoms arXiv:1606.09161v2 [cond-mat.str-el]

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

“…We also study the stripe order, evident away from half-filling, which is naturally viable with R-DMFT. R-DMFT, an extension of DMFT, has been successfully employed to study, e.g., topological systems, interfaces, and trapped correlated systems [42][43][44]. Here, we apply R-DMFT coupled with The paper is structured as follows.…”

Quantum simulation of strongly correlated condensed matter systems

“…The bulk-edge correspondence has been verified for the interaction-driven transition into the QSH state [204,205], while exotic quantum magnetic order was found for larger interaction values, see figure 20. For bosons, on the other hand, it is an open question whether topological (Chern-) insulating states can be realized, since this requires strong interactions from the start.…”

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

“…There, it was found that due to interaction effects quasiparticle peaks are getting closer (corresponding to a narrowing of the gap) which renders the Spin-Hall Conductivity more sensitive to changes in the temperature. Another example of a topological system is the time-reversal invariant Hofsdatdter model which has been studied with negative and positive Hubbard interaction [27][28][29] . The probably most natural framework for the analysis of the Hall conductivity σ xy is the Hubbard model in a finite magnetic field, i.e., the standard Hofsdater model with broken time-reversal symmetry, which has -to the best of our knowledge-not been addressed so far.…”