Quantum phase transition in a 2D XY model
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
In the last decade considerable interest has been dedicated to quantum phase
transitions (QPT), driven by experiments on the cuprate superconductors, the heavy fermions materials, organic conductors, ans related compounds. These transitions occur at zero temperature when a nonthermal parameter like pressure, chemical composition or magnetic field is varied. QPT are believed
to provide keys to many new and exciting phenomena in condensed matter physics. The fluctuations which destroy the long-range order in these transitions are quantum fluctuations which are consequence of the Heisenberg´s uncertainty principle.There are two possibilities for the T > 0 phase diagram of a system near a quantum critical point. In the first the singularity in the free energy is present only at T = O. This is the case for the one dimensional XY model.In the second case there is a line of T>0 phase transition that terminates at the quantum critial point. This will happens for the model that
I will consider here.The physics of the QPT is in general complex. One theoretical model where it can be well undestood is the anisotropic quantum
XY model in one and two dimensions. This model has some similarity with the one describing array of Josephson junctions connecting two superconducting metalic grains. I will present a study of the QPT in the two-dimensional XY model with an XY easy-plane single ion anisotropy using the path-integral formalism. The effects of quantum fluctuations,which renormalize the
parameters of the system, will be taken into account by meansof a self consistent harmonic approximation.