The Integrated Density of States for the Wilson Dirac Operator

TL;DR

This paper proves that the integrated density of states for Wilson Dirac operators in lattice QCD exists and is almost surely independent of the gauge field configuration, assuming the gauge field is ergodic.

Contribution

It establishes the ergodic nature of gauge-dependent Dirac operators and proves the existence and gauge-independence of their integrated density of states in the thermodynamic limit.

Findings

Integrated density of states exists for ergodic gauge fields

Density of states is almost surely independent of gauge configurations

Results apply to Wilson Dirac operators in lattice QCD

Abstract

It is shown that gauge field-dependent fermion Dirac operators from lattice QCD form an ergodic operator family in the probabilistic sense, provided the gauge field is an ergodic random field. As a consequence, the integrated density of states of such Dirac operators in the thermodynamic limit exists and is almost surely independent of the chosen gauge field configuration.