Trace distance and scaling behavior of coupled cavity lattice at finite temperature

TL;DR

This paper investigates how trace distance can identify quantum phase transitions in a finite-temperature coupled cavity lattice, revealing its sensitivity to system parameters and its scaling behavior near critical points.

Contribution

It introduces an alternative approach using trace distance to analyze quantum phase transitions at finite temperature in a Jaynes-Cummings lattice, highlighting its effectiveness as an indicator.

Findings

Trace distance signals critical points at finite low temperatures.

Critical points depend on atom-field interaction and detuning.

Scaling behavior of trace distance derivatives varies with system parameters.

Abstract

We use an alternative approach to study the quantum phase transition in a coupled cavity lattice at finite temperature. As an illustrative example, we investigate the behaviors of the trace distance and quantum phase transition in a Jaynes-Cummings lattice at finite temperature. It is found that the trace distance can be used to describe the critical point of the quantum phase transition at finite low temperatures and the critical points are sensitive to the atom-field interaction strength and the detuning factor. For non-equilibrium states, we demonstrate that the time evolution of the trace distance's maximum value is also a good indicator of the critical points. Moreover, we show that the scaling behavior of derivative of the trace distance at the critical points and the scaling rule are dependent on the external parameters of the Hamiltonian.