It is well known now that the two-dimensional (2D) classical (planar) XY model undergoes Kosterlitz-Thouless (KT) [Kosterlitz:73a] transition at [Gupta:88a], characterized by exponentially divergent correlation length and in-plane susceptibility. The transition, due to the unbinding of vortex-antivortex pairs, is weak; the specific heat has a finite peak above .
Does the two-dimensional quantum XY model go through a phase transition? If so, what type of transition? This is a longstanding problem in statistical physics. The answers are relevant to a wide class of two-dimensional problems such as magnetic insulators, superfluidity, melting, and possibly to the recently discovered high- superconducting transition. Physics in two dimensions is characterized by large fluctuations. Changing from the classical model to the quantum model, additional quantum fluctuations (which are particularly strong in the case of spin-1/2) may alter the physics significantly. A direct consequence is that the already weak KT transition could be washed out completely.