Quantum phase transition of the sub-Ohmic rotor model

TL;DR

This paper studies a quantum rotor model coupled to a sub-Ohmic bath, revealing a phase transition with different critical behaviors depending on the spectral density exponent, and confirms the quantum-to-classical mapping validity.

Contribution

It provides an exact analysis of the quantum phase transition in the sub-Ohmic rotor model at large N, identifying critical behaviors and validating the quantum-classical mapping.

Findings

Identifies nontrivial critical behavior for 1>s>1/2.

Finds mean-field behavior for s<1/2.

Confirms quantum-to-classical mapping for the model.

Abstract

We investigate the behavior of an $N$-component quantum rotor coupled to a bosonic dissipative bath having a sub-Ohmic spectral density $J(\omega) \propto \omega^s$ with $s<1$. With increasing dissipation strength, this system undergoes a quantum phase transition from a delocalized phase to a localized phase. We determine the exact critical behavior of this transition in the large-$N$ limit. For $1>s>1/2$, we find nontrivial critical behavior corresponding to an interacting renormalization group fixed point while we find mean-field behavior for $s<1/2$. The results agree with those of the corresponding long-range interacting classical model. The quantum-to-classical mapping is therefore valid for the sub-Ohmic rotor model.