Z2 characterization for three-dimensional multiband Hubbard models

Abstract

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spinorbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surfaces originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, nontrivially linked nodal line semimetals, and circuit-based quantum simulators.

Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling

“…Further, we use the above effective non-interacting Hamiltonian H T to calculate the Z 2 invariant using the approach employing twisted boundary conditions 39,68,111,118,119 . We consider spin-dependent twisted boundary conditions along the e 1 direction and spin-independent twisted boundary conditions along the e 2 direction.…”

“…Therefore it is of hight interest to study the effect of the local Hubbard interaction on the topological properties of the system. In particular, the following aspects have been studied: the time reversal invariant Hofstadter-Hubbard model [35][36][37][38][39] , the Haldane-Hubbard model [40][41][42][43] , the Kane-Mele-Hubbard model [44][45][46][47] , the interacting Rice-Mele model 48 , the Bernevig-Hughes-Zhang Hubbard model 49,50 , Weyl-Hubbard model 51 , SU(3) systems with artificial gauge fields 52,53 , and the Kondo lattice model [54][55][56] .…”

Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory

“…We use dynamical mean-field theory (DMFT) in order to solve the present many-body problem approximately 28 . In the context of topological systems, DMFT has been used in numerous studies in 2d [29][30][31][32][33][34][35][36][37][38] as well as 3d systems 39,40 . DMFT has been applied recently to WSMs: In Ref.…”