Dynamic critical exponent in quantum long-range models

TL;DR

This paper investigates the critical behavior of quantum long-range models using fractional Lifshitz field theories, focusing on how weak self-interactions influence the dynamic critical exponent at infrared fixed points.

Contribution

It provides the first calculation of corrections to the dynamic critical exponent in fractional Lifshitz theories with weak self-interactions.

Findings

Infrared fixed points exhibit Lifshitz scale invariance.

Lowest-order corrections to the dynamic critical exponent are computed.

Results enhance understanding of quantum long-range critical phenomena.

Abstract

Quantum long-range models at zero temperature can be described by fractional Lifshitz field theories, that is, anisotropic models whose actions are short-range in time and long-range in space. In this paper we study the renormalization of fractional Lifshitz field theories with weakly relevant cubic or quartic self-interactions. Their nontrivial infrared fixed points exhibit Lifshitz scale invariance, and we compute the lowest-order corrections to the dynamic critical exponent.