The Sign Problem is the Solution

TL;DR

This paper demonstrates how oscillations in the unquenched spectral density of the Dirac operator at nonzero chemical potential cause the discontinuity in the chiral condensate, revealing insights into the sign problem.

Contribution

It shows that the oscillatory behavior of the spectral density explains the chiral condensate discontinuity, offering a new perspective on the sign problem in QCD.

Findings

Oscillations in spectral density have volume-dependent periods and amplitudes.

Oscillations cause the discontinuity in the chiral condensate.

The sign problem is linked to these spectral oscillations.

Abstract

The unquenched spectral density of the Dirac operator at $\mu\neq0$ is complex and has oscillations with a period inversely proportional to the volume and an amplitude that grows exponentially with the volume. Here we show how the oscillations lead to the discontinuity of the chiral condensate.