Semiclassical bifurcations and topological phase transitions in a one-dimensional lattice of coupled Lipkin-Meshkov-Glick models

TL;DR

This paper explores the interplay between semiclassical bifurcations and topological phase transitions in a one-dimensional lattice of coupled Lipkin-Meshkov-Glick models, revealing new quantum phases and edge states.

Contribution

It introduces a hybrid semiclassical-topological model that links bifurcations at mean-field level with topological phases in a lattice of Lipkin-Meshkov-Glick models.

Findings

Bifurcations induce diverse ordered quantum phases.

Nontrivial topological phases with edge states emerge.

Quantum fluctuations reveal topological properties.

Abstract

In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are present in our semiclassical-topological hybrid system, allowing us to investigate an interplay between semiclassical bifurcations at mean-field level and topological phases. Our results show that bifurcations of the energy landscape lead to diverse ordered quantum phases. Furthermore, the study of the quantum fluctuations around the mean field solution reveals the existence of nontrivial topological phases. These are characterized by the emergence of localized states at the edges of a chain with open boundary conditions.