Spectral properties of the non-hermitian Wilson-Dirac operator in the Schroedinger functional

TL;DR

This paper investigates the spectral properties of the non-Hermitian Wilson-Dirac operator within the Schrödinger functional framework, providing insights for simulating QCD with advanced Monte Carlo algorithms.

Contribution

It introduces a semi-analytical method to compute the complex spectrum of the non-Hermitian operator and demonstrates how to extract spectral boundary information using polynomial monitoring.

Findings

Computed the spectrum of the free operator with boundary conditions.

Showed how to infer spectral domain boundaries with gauge fields.

Provided groundwork for improved QCD simulations.

Abstract

We report on some preparatory investigations for the simulation of the QCD Schroedinger functional with a non-hermitian polynomial hybrid Monte Carlo algorithm. The complex spectrum of the non-hermitean free operator with SF boundary condititons is computed semianalytically. Then it is shown how one can obtain relevant information on the boundary of the spectral domain also in the presence of nontrivial gaugefields by monitoring the behavior of polynomials in the Wilson operator applied on random vectors.