Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model

TL;DR

This paper investigates the quantum critical behavior of the Dicke model by analyzing ground-state energy, fidelity, and order parameters, revealing universal scaling laws and critical exponents consistent with previous models.

Contribution

It provides a finite size scaling analysis of fidelity susceptibility and ground-state energy derivatives, establishing universality and critical exponents in the Dicke model.

Findings

Correlation length exponent ν=2/3

Fidelity susceptibility and energy derivatives show similar critical behavior

Scaling exponents align with 1/N expansion predictions

Abstract

Within the numerically exact solution to the Dicke model proposed previously, we study the quantum criticality in terms of the ground-state (GS) energy, fidelity, and the order parameter. The finite size scaling analysis for the average fidelity susceptibility (FS) and second derivative of GS energy are performed. The correlation length exponent is obtained to be $\nu=2/3$, which is the same as that in Lipkin-Meshkov-Glick model obtained previously, suggesting the same universality. It is observed that average FS and second derivative of GS energy show similar critical behavior, demonstrating the intrinsic relation in the Dicke model. The scaling behavior for the order parameter and the singular part of the GS energy at the critical point are also analyzed and the obtained exponents are consistent with the previous scaling hypothesis in 1/N expansion scheme.