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

Christof Gattringer,Stefan Solbrig

doi:10.1016/j.physletb.2005.06.042

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 γ5. 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.

Highlights

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term
Lattice fermions with a twisted mass term have gained a lot of attention recently [1, 2, 3, 4]
Appealing for numerical simulations is the fact that a twisted mass term cures the notorious problem with exceptional configurations at a very low cost

Summary

Introduction

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. For twisted mass fermions the interplay of topology and low-lying Dirac eigenmodes has not yet been analyzed. For Wilson fermions fluctuations of real eigenvalues can become large and only for relatively high values of the regular mass are exceptional configurations ruled out.

Results

Conclusion