Bona fide interaction-driven topological phase transition in correlated SPT states

TL;DR

This paper demonstrates a topological phase transition in a correlated electron system driven solely by inter-layer antiferromagnetic interaction, revealing a transition between bosonic symmetry-protected topological states with no mean-field counterpart.

Contribution

The study provides the first large-scale quantum Monte Carlo simulation of a bona fide topological phase transition driven by interactions in a bilayer honeycomb lattice, identifying a transition between QSH and dimer-singlet insulators.

Findings

Identified a topological phase transition driven by inter-layer antiferromagnetic interaction.

At the transition, spin and charge gaps close while single-particle excitations remain gapped.

Transition described by a (2+1)d O(4) nonlinear sigma model with topological term.

Abstract

It is expected that the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo (QMC) simulations, we provide a concrete example of the Kane-Mele-Hubbard (KMH) model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a $xy$-plane antiferromagnetic Mott insulator ($xy$-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a $(2+1)d$ $O(4)$ nonlinear sigma model (NLSM) with {\it exact} $SO(4)$ symmetry, and a topological term at {\it exactly} $\Theta = \pi$. Relevance of this work towards more general interacting SPT states is discussed.