Phonon-induced modification of quantum criticality

TL;DR

This paper investigates how acoustic phonons influence quantum phase transitions in the O(N) model, revealing a critical flavor number that determines whether the transition is second-order or weakly first-order, with finite temperature tricritical behavior.

Contribution

It develops a renormalization group analysis near four dimensions to identify the impact of phonons on quantum criticality in the O(N) model, including the critical flavor number and transition nature.

Findings

For N > 4, the transition remains second-order.

For N ≤ 4, the transition is weakly first-order.

A tricritical point exists at finite temperature for N ≤ 4.

Abstract

We study the effect of acoustic phonons on the quantum phase transition in the O($N$) model. We develop a renormalization group analysis near (3+1) space-time dimensions and derive the RG equations using an $\epsilon$-expansion. Our results indicate that when the number of flavors of the underlying O($N$) model exceeds a critical number $N_c=4$, the quantum transition remains second-order of the Wilson-Fisher type while, for $N\le 4$, it is a weakly first-order transition. We characterize this weakly first-order transition by a length-scale $\xi^*$, below which the behavior appears to be critical. At finite temperatures for $N\le 4$, a tricritical point separates the weakly first-order and second-order transitions.