%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 Energy spectrum for a cylinder geometry as a function of ky %U https://iop.figshare.com/articles/figure/_Energy_spectrum_for_a_cylinder_geometry_as_a_function_of_em_k_sub_y_sub_em_/1012005 %R 10.6084/m9.figshare.1012005.v1 %2 https://ndownloader.figshare.com/files/1479830 %K lattice %K helical edge states %K spectrum %K RDMFT %K topological insulator %K simulation %K interaction %K phase diagram %K Hofstadter %K term %K model %K Atomic Physics %K Molecular Physics %X

Figure 1. Energy spectrum for a cylinder geometry as a function of ky. Bulk spectrum is shown in blue, edge states in red. Artificial magnetic flux is α = 1/10, and γ and λx take values as indicated. Doubly degenerate helical edge states (red) are traversing the bulk gaps.

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