Exploring interacting topological insulator of extended Su-Schrieffer-Heeger model

TL;DR

This paper investigates the many-body topological phases of an extended SSH model with four sublattices, revealing phase transitions and phase diagrams using numerical methods, and discusses experimental realizations with ultracold atoms.

Contribution

It introduces the SSH4 model with four sublattices, maps its phase diagram, and characterizes the nature of phase transitions in interacting topological systems.

Findings

Identified continuous phase transitions between topological and trivial phases.

Mapped the global phase diagram including topological, trivial, and CDW phases.

Showed how spin interactions affect the CDW phase in the SSH4 model.

Abstract

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.