%0 Figure %A P Orth, Peter %A Cocks, Daniel %A Rachel, Stephan %A Buchhold, Michael %A Le Hur, Karyn %A Hofstetter, Walter %D 2013 %T Interacting phase diagram at α = 1/6 as a function of interaction U and staggering λx for various values of spin-mixing γ %U https://iop.figshare.com/articles/figure/_Interacting_phase_diagram_at_1_6_as_a_function_of_interaction_em_U_em_and_staggering_sub_em_x_em_su/1012008 %R 10.6084/m9.figshare.1012008.v1 %2 https://iop.figshare.com/ndownloader/files/1479833 %K lattice %K model %K qsh %K ni %K topological insulator %K simulation %K interaction %K phase diagram %K semi %K Hofstadter %K term %K RDMFT %K Atomic Physics %K Molecular Physics %X

Figure 4. Interacting phase diagram at α = 1/6 as a function of interaction U and staggering λx for various values of spin-mixing γ. We find the (semi)-metallic regime (Metal), magnetically ordered state (Mag), NI and QSH state.

Abstract

Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter–Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin–orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from a normal to a topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spin–orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.

%I IOP Publishing