01529nas a2200145 4500008004100000245007400041210006900115260001500184490000800199520104100207100002601248700001701274700002201291856007001313 2020 eng d00aQuantum Lifshitz criticality in a frustrated two-dimensional XY model0 aQuantum Lifshitz criticality in a frustrated twodimensional XY m c01/09/20200 v1013 a
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 NĂ©el 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.