Domain-wall and overlap fermions at nonzero quark chemical potential

TL;DR

This paper extends the overlap and domain-wall fermion formalisms to include nonzero quark chemical potential, ensuring key properties like anomaly-index relations are preserved in the continuum limit.

Contribution

It introduces a construction of the overlap Dirac operator at nonzero chemical potential within the domain-wall fermion framework and proves its key properties.

Findings

Reproduces earlier overlap operator results at infinite fifth dimension

Includes a bare quark mass and considers the continuum limit

Maintains the anomaly-index relation at nonzero chemical potential

Abstract

We have recently given a construction of the overlap Dirac operator at nonzero quark chemical potential. Here, we introduce a quark chemical potential in the domain-wall fermion formalism and show that our earlier result is reproduced if the extent of the fifth dimension is taken to infinity and its lattice spacing is taken to zero. We also extend this result to include a bare quark mass, consider its continuum limit, and prove a number of properties of the overlap operator at nonzero quark chemical potential. In particular, we show that the relation between the anomaly and the index of the overlap operator remains valid.