Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model

TL;DR

This paper investigates how bath-induced many-body interactions affect the topological phases of the SSH model, using a novel method to treat system-bath interactions and identify the mechanisms behind phase modifications.

Contribution

It introduces the RCPT method to analyze strong system-bath couplings in the SSH model, revealing bath-induced many-body interactions as key to phase behavior.

Findings

Bath coupling extends the topological and trivial phase regions.

Many-body interactions are generated by bath coupling and influence phase stability.

The method can distinguish topological phases even at finite temperature.

Abstract

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it non-perturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. We also study the effect of on-site staggered potentials on the SSH phase diagram, and discuss extensions of our method to higher dimensions.