Universality and Crossovers for Quantum-Criticality in 2d metals

TL;DR

This paper generalizes classical-criticality crossover theory to quantum-criticality in 2d metals, explaining universal fluctuation behaviors and thermodynamics across various compounds and extending to disorder effects.

Contribution

It introduces a simple framework for understanding quantum-critical crossovers and fluctuations in 2d metals, connecting them to the quantum xy model and extending Harris criteria for disorder.

Findings

Quantum-critical fluctuations resemble the quantum xy model.

Observed T ln T specific heat at criticality is explained.

Universal fluctuation behavior across cuprates, heavy-fermion, and Fe-based metals.

Abstract

A simple generalization of the theory of crossovers in classical-criticality to quantum-criticality gives that, a Heisenberg model with a small anisotropy favoring planar order has a cross-over towards the fixed point of the xy model in the temperature direction which is very rapid compared to those in the orthogonal directions, if the temporal correlation length is much larger than the spatial correlation length, i.e. for a large dynamic exponent $z$. At the other end of the flow, the stability of the fixed point of the quantum xy model coupled to fermions is exponentially enhanced in the temperature direction. This is used to explain why the quantum-critical fluctuations of all measured 2d anti-ferromagnetic compounds - cuprates, heavy-fermion and Fe-based metals shows the characteristic fluctuations of the quantum xy model, and have the same anomalous transport and thermodynamic properties as the cuprates and twisted WSe$_2$ and Graphene. We segue briefly to the range of extended quantum-criticality due to disorder by generalizing the Harris criteria as well, using the properties of the quantum xy model. The observed $T \ln T$ specific heat at criticality is derived quite simply using the same methods which derive the cross-overs. This paper is written for the commemoration volume for Jan Zaanen whom I knew very well, starting from his days as a post-doc at Bell labs to his career as a distinguished Professor at Leiden.