Order-Parameter Correlation Functions in Quantum Critical Phenomena

TL;DR

This paper examines the behavior of order-parameter correlation functions at quantum critical points, revealing that without particle-hole symmetry, the equal-time correlations do not exhibit diverging correlation lengths, contrary to traditional beliefs.

Contribution

The study demonstrates that in quantum critical systems lacking particle-hole symmetry, equal-time correlation functions do not diverge, supported by Monte Carlo simulations of the quantum rotor model.

Findings

Equal-time correlation functions do not diverge at criticality without particle-hole symmetry.

Monte Carlo simulations confirm the non-diverging correlation length.

Challenges conventional understanding of quantum critical correlations.

Abstract

We investigate the functional form of the order-parameter (two-point) correlation function in quantum critical phenomena. Contrary to the common lore, when there is no particle-hole symmetry we find that the equal-time correlation function at criticality does not display a diverging correlation length. We illustrate our conclusions by Monte Carlo calculations of the quantum rotor model in $d=2$ space dimensions