Remnant index theorem and low-lying eigenmodes for twisted mass fermions

TL;DR

This paper investigates the spectral properties of twisted mass lattice Dirac operators, revealing how the twist modifies eigenvalue distributions, affects zero modes, and supports a remnant index theorem, with implications for understanding topological features in lattice QCD.

Contribution

It introduces an analysis of the low-lying spectrum of twisted mass fermions, demonstrating the spectral structure and topological implications, including a remnant index theorem for Ginsparg-Wilson operators.

Findings

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

Eigenmodes have non-zero gamma-5 matrix elements.

Topological modes are located at the edges of spectral arcs.

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.