Quantum Phase Transitions and Conserved Charges

TL;DR

This paper investigates the universal behavior of conserved charge densities near zero-temperature quantum phase transitions, introducing a generalized Wilson ratio that captures non-linear responses and has broad implications for various transition types.

Contribution

It introduces a universal generalized Wilson ratio for conserved charges near quantum critical points and explores its implications for different types of quantum phase transitions.

Findings

The generalized Wilson ratio is a universal function of H/T.

Computations on model systems support the universality of the ratio.

Implications for transitions with conserved charge order parameters are discussed.

Abstract

The constraints on the scaling properties of conserved charge densities in the vicinity of a zero temperature ($T$), second-order quantum phase transition are studied. We introduce a generalized Wilson ratio, characterizing the non-linear response to an external field, $H$, coupling to any conserved charge, and argue that it is a completely universal function of $H/T$: this is illustrated by computations on model systems. We also note implications for transitions where the order parameter is a conserved charge (as in a $T=0$ ferromagnet-paramagnet transition).