Fermionic fields in the pseudoparticle approach

TL;DR

This paper extends the pseudoparticle approach, a numerical method for path integrals, to include fermionic fields, demonstrated through the 1+1D Gross-Neveu model's phase diagram and chiral condensate.

Contribution

The paper introduces a novel way to incorporate fermionic fields into the pseudoparticle approach, expanding its applicability to fermionic theories.

Findings

Successfully computed the phase diagram of the Gross-Neveu model

Determined the chiral condensate in the crystal phase

Validated the method against known results

Abstract

The pseudoparticle approach is a numerical method to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number of localized building blocks (pseudoparticles), and to replace the functional integration by an integration over the pseudoparticle degrees of freedom. In previous papers we have successfully applied the pseudoparticle approach to SU(2) Yang-Mills theory. In this work we discuss the inclusion of fermionic fields in the pseudoparticle approach. To test our method, we compute the phase diagram of the 1+1-dimensional Gross-Neveu model in the large-N limit as well as the chiral condensate in the crystal phase.