Poisson to Random Matrix Transition in the QCD Dirac Spectrum

TL;DR

This paper investigates how the low-lying eigenmodes of the QCD Dirac operator transition from delocalized, random matrix statistics at low temperature to localized, Poisson statistics at higher temperatures, using lattice QCD simulations.

Contribution

It demonstrates the temperature-driven localization transition of Dirac eigenmodes and analyzes the scaling of the mobility edge in the continuum limit.

Findings

Low-temperature eigenmodes are delocalized with random matrix statistics.

High-temperature eigenmodes become localized with Poisson statistics.

The mobility edge increases sharply with temperature and scales in the continuum limit.

Abstract

At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to consist of delocalized modes that are described by random matrix statistics. In the present paper we show that the nature of these eigenmodes changes drastically when the system is driven through the finite temperature cross-over. The lowest Dirac modes that are delocalized at low temperature become localized on the scale of the inverse temperature. At the same time the spectral statistics changes from random matrix to Poisson statistics. We demonstrate this with lattice QCD simulations using 2+1 flavors of light dynamical quarks with physical masses. Drawing an analogy with Anderson transitions we also examine the mobility edge separating localized and delocalized modes in the spectrum. We show that it scales in the continuum limit and increases sharply with the temperature.