Reentrant topological phases and entanglement scalings in moir\'e-modulated extended Su-Schrieffer-Heeger Model

TL;DR

This paper explores reentrant topological phase transitions in a moiré-modulated extended SSH model, revealing universal properties, bulk-boundary correspondence, and entanglement scaling through analytical and numerical methods.

Contribution

It provides the first analytical and numerical analysis of reentrant phase transitions and their universality in moiré-modulated topological systems.

Findings

Reentrant phase transitions are analytically explained for a simplified model.

Numerical phase boundaries are mapped in the thermodynamic limit.

Bulk-boundary correspondence is confirmed via zero-energy edge modes and entanglement spectrum.

Abstract

Recent studies of moir\'e physics have unveiled a wealth of opportunities for significantly advancing the field of quantum phase transitions. However, properties of reentrant phase transitions driven by moir\'e strength are poorly understood. Here, we investigate the reentrant sequence of phase transitions and the invariant of universality class in moir\'e-modulated extended Su-Schrieffer-Heeger (SSH) model. For the simplified case with intercell hopping $w=0$, we analytically derive renormalization relations of Hamiltonian parameters to explain the reentrant phenomenon. For the general case, numerical phase boundaries are calculated in the thermodynamic limit. The bulk boundary correspondence between zero-energy edge modes and entanglement spectrum is revealed from the degeneracy of both quantities. We also address the correspondence between the central charge obtained from entanglement entropy and the change in winding number during the phase transition. Our results shed light on the understanding of universal characteristics and bulk-boundary correspondence for moir\'e induced reentrant phase transitions in 1D condensed-matter systems.