Identifying the phases of Kane-Mele Hubbard Hamiltonian in momentum space: A many-body configuration interaction study

TL;DR

This study uses a many-body configuration interaction approach to analyze phase transitions in the Kane-Mele Hubbard model, revealing a shift in charge gap minima indicative of a topological phase transition in momentum space.

Contribution

It introduces a numerical CI method to identify topological phase transitions in strongly correlated systems through momentum space analysis.

Findings

Charge gap minima shift from Brillouin zone boundary to Dirac point during transition

Spin sector remains topologically invariant across phases

Provides an alternative numerical method to detect topological transitions

Abstract

We investigate the magnetic and conduction properties of Kane-Mele Hubbard model in quasi one-dimensional honeycomb ribbon systems at half-filling by varying the strength of both spin-orbit interaction and on-site Coulomb correlation term. We use the numerical many-body configuration interaction (CI) method to investigate the dispersions of charge and spin gaps along with the momentum resolved spin-density profile over the full Brillouin zone. While the spin sector retains its topological nature at all values of spin-orbit coupling and Hubbard term, we report a new signature of the topological phase transition in the charge sector. This phase transition from a topological band insulating phase to a antiferromagnetically ordered Mott insulating phase is characterized by a shift of the many-body charge gap minima from Brillouin zone boundary to Dirac point. Our results provide a better understanding of the shifting of the gap-closing point in the momentum space which was reported in an earlier mean-field study of the same model and suggests an alternative numerical route to detect topological phase transition in strongly-correlated systems in terms of their momentum space behaviors.