Thermodynamics and entanglement entropy of the non-Hermitian SSH model

TL;DR

This paper explores the thermodynamic and entanglement properties of the non-Hermitian SSH model, revealing novel critical behaviors and boundary effects associated with topological phase transitions and complex energy phases.

Contribution

It introduces a thermodynamic analysis of the non-Hermitian SSH model, uncovering new physics in boundary contributions and phase transitions involving complex energies.

Findings

Boundary effects analyzed via Hill's thermodynamics.

Heat capacity linked to central charge at topological transitions.

Discovery of an unexpected critical behavior in complex energy phases.

Abstract

Topological phase transitions are found in a variety of systems and were shown to be deeply related with a thermodynamic description through scaling relations. Here, we investigate the entanglement entropy, which is a quantity that captures the central charge of a critical model and the thermodynamics of the non-reciprocal Su-Schrieffer-Heeger (SSH) model. Although this model has been widely studied, the thermodynamic properties reveal interesting physics not explored so far. In order to analyze the boundary effects of the model, we use Hill's thermodynamics to split the grand potential in two contributions: the extensive one, related to the bulk, and the subdivision one, related to the boundaries. Then, we derive the thermodynamic entropy for both, the edges and the bulk and the heat capacity for the bulk at the topological phase transitions. The latter is related to the central charge when the underlying theory is a conformal field theory, whereas the first reveals the resilience of the topological edge states to finite temperatures. The phase transition between phases that are adiabatically connected with the Hermitian SSH model display the well-known behaviour of systems within the Dirac universality class, but the transition between phases with complex energies shows an unexpected critical behavior, which signals the emergence of an imaginary time crystal.