Low-lying spectrum for lattice Dirac operators with twisted mass

TL;DR

This paper investigates the spectral properties of lattice Dirac operators with twisted mass, revealing how the twist influences eigenvalues and modes, especially in relation to topology and the confined phase.

Contribution

It provides a detailed analysis of the low-lying spectrum and eigenmodes of twisted mass lattice Dirac operators, including the spectral location and topological mode behavior.

Findings

Eigenvalues are expelled from a strip in the complex plane due to the twist.

Eigenmodes have non-zero gamma-5 matrix elements.

Topological modes are located at the edges of spectral arcs and follow a remnant index theorem.

Abstract

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with gamma-5. For a twisted Ginsparg-Wilson operator the spectrum is located on two arcs in the complex plane. Modes due to non-trivial topological charge of the underlying gauge field have their eigenvalues at the edges of these arcs and obey a remnant index theorem. For configurations in the confined phase we find that the twist mainly affects the zero modes, while the bulk of the spectrum is essentially unchanged.