Quantum Lifshitz criticality in a frustrated two-dimensional XY model

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 Néel 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.

Colossal quasiparticle radiation in the Lifshitz spin liquid phase of a two-dimensional quantum antiferromagnet

“…As discussed in Ref. [12], the one loop self energy simply renormalizes the spin stiffness, and otherwise does not have a qualitative effect on the nature of the quasiparticles. At two loop level, the self energy has an imaginary part generated by the diagram in Fig.…”

“…These two phases are separated classically by the Lifshitz point ρ = 0. However, one of us has previously shown that quantum corrections due to the long range interactions lead to a nontrivial renormalization of the spin stiffness ρ → ρ r [12]. For the purposes of this paper, it suffices to note that the LP actually corresponds to ρ r = 0, and from hereon, we will assume that all renormalization has been taken care of and suppress the subscript.…”

“…In fact, the dominant contribution comes from when the momentum is evenly distributed among the decay products. 2) Spiral order only affects the linear part of the quasiparticle dispersion [12]. 3) If b 1,2 q 2 ρ, then the linear terms in the dispersion are irrelevant.…”

“…In contrast to other spin liquids, the LSL is connected to the collinear and spiral ordered phases by continuous phase transitions. However, one of us has demonstrated that unlike the O(3) symmetric case, the LSL in an easy-plane XY antiferromagnet only exists at the LP [12].…”

“…For clarity, we also summarize some general considerations discussed in detail in Ref. [12]. In Sec.…”