Quantum Lifshitz criticality in a frustrated two-dimensional XY model

TL;DR

This paper investigates the quantum phase transition in a frustrated 2D XY model, revealing that a spin liquid state exists only at the critical point and analyzing critical exponents and topological effects.

Contribution

It provides a field theory solution for the Lifshitz quantum phase transition in the 2D XY model, clarifying the conditions for spin liquid existence.

Findings

Spin liquid exists only at the critical point in the XY model.

Calculated nonuniversal critical exponents at zero temperature.

Discussed the role of topological excitations at finite temperature.

Abstract

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY-model. Specifically, we show that, unlike the SU(2) symmetric Lifshitz case, in the XY-model the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Neel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.