Quantum criticality in the two-dimensional dissipative quantum XY model-II

TL;DR

This paper investigates the phase transitions and critical behavior of the two-dimensional dissipative quantum XY model, revealing a change in dynamical critical exponent and the nature of correlations as dissipation varies.

Contribution

It extends Monte Carlo studies to explore how dissipation influences criticality, phase diagram, and correlation functions, including the effects of different dissipation forms.

Findings

Transition from z=1 to z→∞ criticality driven by topological defects.

Power-law singularities in correlations as a function of energy ratio at fixed large dissipation.

The nature of the transition depends on the form of dissipation, especially the Caldeira-Leggett type.

Abstract

Earlier Monte-Carlo calculations on the dissipative two-dimensional XY model are extended in several directions. We study the phase diagram and the correlation functions when dissipation is very small, where it has properties of the classical 3D-XY transition, i.e. one with a dynamical critical exponent $z=1$. The transition changes from $z=1$ to the class of criticality with $z \to \infty$ driven by topological defects, discovered earlier, beyond a critical dissipation. We also find that the critical correlations have power-law singularities as a function of tuning the ratio of the kinetic energy to the potential energy for fixed large dissipation, as opposed to essential singularities on tuning dissipation keeping the former fixed. A phase with temporal disorder but spatial order of the Kosterlitz-Thouless form is also further investigated. We also present results for the transition when the allowed Caldeira-Leggett form of dissipation and the allowed form of dissipation coupling to the compact rotor variables are both included. The nature of the transition is then determined by the Caldeira-Leggett form.