Criticality in correlated quantum matter

TL;DR

This paper explores the persistence of quantum critical effects at finite temperatures in correlated quantum systems, revealing high-temperature regimes where universal scaling functions apply, and predicts a specific relationship between superfluid density and transition temperature in cuprates.

Contribution

It demonstrates that quantum criticality effects can persist at surprisingly high temperatures and establishes a testable relation between superfluid density and transition temperature in cuprates.

Findings

Quantum critical effects can persist at high temperatures.

A universal scaling relation between $T_c$ and $ ho_s(0)$ is proposed.

Different exponents at the edges of the superconducting dome indicate distinct QCPs.

Abstract

At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examining exact solutions of models of correlated systems and find that the temperature can be surprisingly high. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, $\rho_{s}(0)$, and the transition temperature, $T_{c}$, of the cuprates are related by $T_{c}\propto\rho_{s}(0)^y$, where the exponent $y$ is different at the two edges of the superconducting dome, signifying the respective QCPs. This relationship can be tested in high quality crystals.