# Universal scaling and critical exponents of the anisotropic quantum Rabi model

## TL;DR

This paper analyzes the phase transitions and critical behavior of the anisotropic quantum Rabi model, revealing universal properties and novel features across different coupling regimes relevant to light-matter systems.

## Contribution

It provides a comprehensive phase diagram, scaling functions, and critical exponents for the anisotropic quantum Rabi model, demonstrating universality across anisotropy levels.

## Key findings

- Universality class remains the same at finite anisotropy and isotropic limit.
- Identification of superradiance-induced effective mass freezing.
- Discontinuous scaling functions observed in the Jaynes-Cummings limit.

## Abstract

We investigate first- and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating- and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite? anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are relevant in a variety of systems able to realize strong coupling between light and matter, such as circuit QED setups where a finite anisotropy appears quite naturally.