A Numerical Study of the 2-Flavour Schwinger Model with Dynamical Overlap Hypercube Fermions

TL;DR

This paper presents numerical analysis of the 2-flavour Schwinger model using a novel overlap hypercube fermion approach, demonstrating efficient computation, spectral measurements, and topological insights relevant for lattice QCD simulations.

Contribution

Introduction of an overlap hypercube fermion operator with excellent locality and scaling, enabling efficient dynamical simulations and spectral analysis in the Schwinger model.

Findings

Efficient Hybrid Monte Carlo force due to hypercube kernel

Measurement of Dirac spectrum and chiral condensate

Analysis of topological sectors and susceptibility

Abstract

We present numerical results for the 2-flavour Schwinger model with dynamical chiral lattice fermions. We insert an approximately chiral hypercube Dirac operator into the overlap formula to construct the overlap hypercube operator. This is an exact solution to the Ginsparg-Wilson relation, with an excellent level of locality and scaling. Due to its similarity with the hypercubic kernel, a low polynomial in this kernel provides a numerically efficient Hybrid Monte Carlo force. We measure the microscopic Dirac spectrum and discuss the corresponding scale-invariant parameter, which takes a surprising form. This is an interesting case, since Random Matrix Theory is unexplored for this setting, where the chiral condensate {\Sigma} vanishes in the chiral limit. We also measure {\Sigma} and the "pion" mass, in distinct topological sectors. In this context we discuss and probe the topological summation of observables by various methods, as well as the evaluation of the topological susceptibility. The feasibility of this summation is essential for the prospects of dynamical overlap fermions in QCD.