Z2 characterization for three-dimensional multiband Hubbard models

TL;DR

This paper introduces numerical methods to characterize topological phases in three-dimensional multiband Hubbard models, revealing interaction-stabilized topological states and surface asymmetries, with implications for future quantum materials research.

Contribution

It presents new numerical techniques for topological characterization and demonstrates their application to interaction effects in 3D Hubbard models, including stabilization of topological phases.

Findings

Identification of weak and strong topological insulators

Discovery of a nodal line semimetal phase

Interaction stabilizes topological states

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 spin-orbit 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 surface 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, non-trivially linked nodal line semimetals and circuit-based quantum simulators.