Topological phases of extended Su-Schrieffer-Heeger-Hubbard model

TL;DR

This paper explores the extended SSHH model with next-nearest neighbor hopping, revealing rich topological phases and edge states using advanced quantum Monte Carlo methods, and examines how magnetic fields influence these properties.

Contribution

It introduces a comprehensive study of the extended SSHH model with next-nearest neighbor hopping, highlighting its topological phases and the effects of magnetic fields using CP-AFQMC.

Findings

The model exhibits robust topological edge states against interactions.

Long-range spin correlations and near-zero R'enyi entropy are observed at half-filling.

External magnetic fields disrupt anti-ferromagnetic order, restoring spin correlation.

Abstract

Despite extensive studies on the one-dimensional Su-Schrieffer-Heeger-Hubbard (SSHH) model, the variant incorporating next-nearest neighbour hopping remains largely unexplored. Here, we investigate the ground-state properties of this extended SSHH model using the constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) method. We show that this model exhibits rich topological phases, characterized by robust edge states against interaction. We quantify the properties of these edge states by analyzing spin correlation and second-order R\'enyi entanglement entropy. The system exhibits long-range spin correlation and near-zero R\'enyi entropy at half-filling. Besides, there is a long-range anti-ferromagnetic order at quarter-filling. Interestingly, an external magnetic field disrupts this long-range anti-ferromagnetic order, restoring long-range spin correlation and near-zero R\'enyi entropy. Furthermore, our work provides a paradigm studying topological properties in large interacting systems via the CP-AFQMC algorithm.