Effective Field Theories and Finite-temperature Properties of Zero-dimensional Superradiant Quantum Phase Transitions

TL;DR

This paper clarifies how zero-dimensional superradiant quantum phase transitions can be understood within effective field theories, demonstrating their compatibility with statistical physics through analysis of the Rabi and Dicke models.

Contribution

It derives the effective field theories for zero-dimensional superradiant transitions and shows their second-order nature, resolving previous inconsistencies with statistical physics.

Findings

Effective field theory of the Rabi model is a free scalar field.

Zero-dimensional superradiant transition is second-order.

Numerical simulations confirm theoretical predictions.

Abstract

The existence of zero-dimensional superradiant quantum phase transitions seems inconsistent with conventional statistical physics. This work clarifies this apparent inconsistency. We demonstrate the corresponding effective field theories and finite-temperature properties of light-matter interacting systems, and show how this zero-dimensional quantum phase transition occurs. We first focus on the Rabi model, which is a minimum model that hosts a superradiant quantum phase transition. With the path integral method, we derive the imaginary-time action of the photon degrees of freedom. We also define a dynamical critical exponent as the rescaling between the temperature and the photon frequency, and perform dimensional analysis to the effective action. The dynamical critical exponent shows that the effective theory of the Rabi model is a free scalar field, where a true second-order quantum phase transition emerges. These results are also verified by numerical simulations of imaginary-time correlation functions of the order parameter. Furthermore, we also generalize this method to the Dicke model. Our results make the zero-dimensional superradiant quantum phase transition compatible with conventional statistical physics, and pave the way to understand it in the perspective of effective field theories.