Universally diverging Grueneisen parameter and the magnetocaloric effect close to quantum critical points

TL;DR

This paper investigates the divergence of the Gr"uneisen ratio near quantum critical points, revealing universal scaling behaviors and corrections in metallic systems, with implications for measuring critical exponents and the magnetocaloric effect.

Contribution

It establishes universal relations for the Gr"uneisen ratio and magnetocaloric effect near quantum critical points, including corrections to scaling in metallic systems.

Findings

The Gr"uneisen ratio diverges as a universal power law at quantum critical points.

Universal relations connect the Gr"uneisen ratio to critical exponents and pressure.

Corrections to scaling are determined for metallic quantum critical points.

Abstract

At a generic quantum critical point, the thermal expansion $\alpha$ is more singular than the specific heat $c_p$. Consequently, the "Gr\"uneisen ratio'', $\GE=\alpha/c_p$, diverges. When scaling applies, $\GE \sim T^{-1/(\nu z)}$ at the critical pressure $p=p_c$, providing a means to measure the scaling dimension of the most relevant operator that pressure couples to; in the alternative limit $T\to0$ and $p \ne p_c$, $\GE \sim \frac{1}{p-p_c}$ with a prefactor that is, up to the molar volume, a simple {\it universal} combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect $(1/T)\partial T/\partial H|_S$. Finally, we determine the corrections to scaling in a class of metallic quantum critical points.