Phase diagram and quantum-criticality of the two dimensional dissipative quantum XY model

TL;DR

This paper analyzes the phase diagram and quantum-critical behavior of the 2D dissipative quantum XY model, revealing unique properties of quantum critical fluctuations and their relevance to high-temperature superconductivity.

Contribution

It provides a renormalization group analysis of the model in terms of topological excitations, explaining previously observed Monte Carlo results and elucidating the role of space-time metric flow.

Findings

Quantum critical fluctuations are separable in space and time.

Spatial correlation length scales logarithmically with temporal correlation length.

Existence of a phase with spatial order but no temporal order.

Abstract

The two-dimensional dissipative quantum XY model is applicable to the quantum-critical properties of diverse experimental systems, ranging from the superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, to the loop-current order transition in the cuprates. We solve the re-expression of this model in terms of topological excitations: vortices and a variety of instantons, by renormalization group methods. The calculations explain the extraordinary properties of the model discovered in Monte-Carlo calculations: the separability of the quantum critical fluctuations (QCF) in space and time, the spatial correlation length proportional to logarithm of the temporal correlation length near the transition from disordered to the fully ordered state, and the occurrence of a phase with spatial order without temporal order. They are intimately related to the flow of the metric of time in relation to the metric of space, i.e. of the dynamical critical exponent $z$. These properties appear to be essential in understanding the strange metallic phase found in a variety of quantum-critical transitions as well as the accompanying high temperature superconductivity.