Complex spectrum of spin models for finite-density QCD

TL;DR

This paper analyzes the complex eigenvalue spectrum of the transfer matrix in lattice QCD at finite density, revealing how non-Hermiticity leads to complex conjugate pairs and oscillatory correlations, with implications for observable phenomena.

Contribution

It demonstrates that charge conjugation symmetry constrains transfer matrix eigenvalues to be real or complex conjugates, explaining oscillatory behavior in Polyakov loop correlations at finite density.

Findings

Eigenvalues are real or form complex conjugate pairs due to symmetry.

Complex eigenvalues cause damped oscillations in correlation functions.

The effect is predicted to be observable in lattice QCD simulations.

Abstract

We consider the spectrum of transfer matrix eigenvalues associated with Polyakov loops in lattice QCD at strong coupling. The transfer matrix at finite density is non-Hermitian, and its eigenvalues become complex as a manifestation of the sign problem. We show that the symmetry under charge conjugation and complex conjugation ensures that the eigenvalues are either real or part of a complex conjugate pair, and the complex pairs lead to damped oscillatory behavior in Polyakov loop correlation functions, which also appeared in our previous phenomenological models using complex saddle points. We argue that this effect should be observable in lattice simulations of QCD at finite density.