Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension

TL;DR

This study investigates the interplay of interactions and topology in a one-dimensional two-orbital Hubbard model, revealing complex phase transitions including trivial, topological, and various insulating phases through variational and DMRG methods.

Contribution

It provides the first detailed analysis of interaction-induced phases and phase transitions in a 1D topological multi-orbital Hubbard model, highlighting emergent intermediate insulators.

Findings

Finite Hubbard-U induces a smooth crossover to a Haldane insulator.

An intermediate gapless spin excitation phase appears between trivial and topological states.

Nearest-neighbor repulsion stabilizes different charge-density wave insulators.

Abstract

We explore the ground-state properties of a one-dimensional model with two orbitals per site, where, in addition to atomic energies $\pm M$, intra- and inter-orbital hoppings, the intra-orbital Hubbard ($U$) and nearest-neighbor density-density ($V$) repulsions are included. Our results are primarily based on a Jastrow-Slater wave function and variational Monte Carlo methods, but also corroborated by density-matrix renormalization group calculations. In the non-interacting limit, when varying $M>0$, a gapless point separates a trivial phase from a topological one. The inclusion of a finite Hubbard-$U$ repulsion does not give rise to any phase transition within the topological region, inducing a smooth crossover into a Haldane (spin gapped) insulator; notably, the string-order parameter, which characterizes the latter phase, is already finite in the non-interacting limit. Most importantly, at finite values of $U$, the transition between the trivial and topological states is not direct, since an emergent insulator, which shows evidence of sustaining gapless spin excitations, intrudes between them. A small $V$ interaction further stabilizes the intermediate insulator, while a sufficiently large value of this nearest-neighbor repulsion gives rise to two different charge-density wave insulators, one fully gapped and another still supporting gapless spin excitations. Our results demonstrate the richness of multi-orbital Hubbard models, in the presence of a topologically non-trivial band structure, and serve as a basis for future investigations on similar two-dimensional models.