A Non-Perturbative Renormalization Group approach to quantum XY spin models

Abstract: We present a Lattice Non-Perturbative Renormalization Group (NPRG) approach to quantum XY spin models by using a mapping onto hardcore bosons. The NPRG takes as initial condition of the renormalization group flow the (local) limit of decoupled sites, allowing us to take into account the hardcore constraint exactly. The initial condition of the flow is equivalent to the large $S$ classical results of the corresponding spin system. Furthermore, the hardcore constraint is conserved along the RG flow, and we can describe both local and long-distance fluctuations in a non-trivial way. We discuss a simple approximation scheme, and solve the corresponding flow equations. We compute both the zero-temperature thermodynamics and the finite temperature phase diagram on the square and cubic lattices. The NPRG allows us to recover the correct critical physics at finite temperature in two and three dimensions. The results compare well with numerical simulations.