Lifshitz critical points meet Zamolodchikov perturbation theory

TL;DR

This paper explores Lifshitz critical points in lattice models using Zamolodchikov's perturbation theory, revealing a manifold of fixed points and emergent symmetry in a coupled minimal model CFT system.

Contribution

It introduces a controlled approach to study anisotropic Lifshitz critical behavior via large m expansion of coupled minimal models, uncovering new fixed points and symmetry emergence.

Findings

Existence of a manifold of Lifshitz fixed points

Emergent rotational symmetry in the infrared

Controlled analysis using Zamolodchikov's large m expansion

Abstract

Critical points of classical and quantum lattice models are often described by scale-invariant Lifshitz theories which are anisotropic in the continuum limit, as characterized by a dynamical critical exponent $z\neq1$. This type of critical behavior can in principle be studied by deforming ordinary $z=1$ conformal field theories (CFTs) by relevant vector operators breaking the rotational/Lorentz symmetry. In this short note, we consider a two-dimensional system of coupled minimal model CFTs $\mathcal{M}_{m,m+1}$ which realizes this perspective in a controlled fashion via Zamolodchikov's large $m$ expansion. The model turns out to exhibit interesting properties, including a manifold of interacting Lifshitz fixed points and emergent rotational symmetry in the infrared.