Entanglement and Topology in Su-Schrieffer-Heeger Cavity Quantum Electrodynamics

TL;DR

This paper investigates how cavity photon-mediated non-local interactions affect the stability of topological phases in the SSH model, revealing that edge states remain stable and entanglement follows an area law despite long-range correlations.

Contribution

It demonstrates the stability of topological edge states in the SSH model under cavity interactions and introduces a framework for analyzing entanglement and correlations in topological cavity materials.

Findings

Edge states remain stable under cavity interactions

Ground state entanglement entropy follows an area law

Long-range correlations do not destabilize topological phases

Abstract

Cavity materials are a frontier to investigate the role of light-matter interactions on the properties of electronic phases of matter. In this work, we raise a fundamental question: can non-local interactions mediated by cavity photons destabilize a topological electronic phase? We investigate this question by characterizing entanglement, energy spectrum and correlation functions of the topological Su-Schrieffer-Heeger (SSH) chain interacting with an optical cavity mode. Employing density-matrix renormalization group (DMRG) and exact diagonalization (ED), we demonstrate the stability of the edge state and establish an area law scaling for the ground state entanglement entropy, despite long-range correlations induced by light-matter interactions. These features are linked to gauge invariance and the scaling of virtual photon excitations entangled with matter, effectively computed in a low-dimensional Krylov subspace of the full Hilbert space. This work provides a framework for characterizing novel equilibrium phenomena in topological cavity materials.