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

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.

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• Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu${}_2$Si${}_2$
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• Loop current fluctuations and quantum critical transport
• Quantum criticality in the two-dimensional dissipative quantum XY model-II
• Dynamic structure function of some singular Fermi-liquids
• Quantum critical singularities in two-dimensional metallic XY ferromagnets
• A Local Quantum Phase Transition in YFe${}_2$Al${}_{10}$
• Anomalous quantum-critical spin dynamics in YFe2Al10
• Renormalizations in unconventional superconducting states born of normal and singular Fermi-liquids
• Quantum-critical resistivity of strange metals in a magnetic field
• Quantum-critical transport in marginal Fermi liquids
• Suppression of superfluidity by dissipation -- An application to failed superconductor