Universality and Scaling Properties of Correlation Functions Near a Quantum Phase Transition

TL;DR

This paper explores the universal scaling behaviors of correlation functions and entanglement near quantum phase transitions, revealing that correlation functions can indicate critical points without predefined order parameters.

Contribution

It demonstrates that correlation functions exhibit similar divergence and scaling as entanglement, and can identify quantum critical points independently of entanglement presence.

Findings

Correlation functions show logarithmic divergence near critical points.

Finite size scaling behaviors of correlation functions mirror those of entanglement.

Correlation functions can detect quantum critical points without pre-assumed order parameters.

Abstract

In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of correlation functions with respect to the parameter that drives the quantum phase transitions, exhibit logarithmic divergence and finite size scaling the same as entanglement. In other words the non-analytic and finite size scaling behaviors of entanglement is not its intrinsic properties and inherit from the non-analytic and scaling behaviors of correlation functions and surveying at least the nearest neighbor correlation functions could specify the scaling and divergence properties of entanglement. However we show that the correlation functions could capture the quantum critical point without pre-assumed order parameters even for the cases where the two-body entanglement is absent.