Density of states approach for lattice field theory with topological terms

TL;DR

This paper introduces a density of states method with open boundary conditions to address the complex action problem in lattice gauge theories with topological terms, demonstrated on U(1) and SU(2) models.

Contribution

The paper develops a novel DoS approach using open boundary conditions to handle topological terms in lattice field theories, enabling regular density functions and potential application to QCD.

Findings

Validated the method on 2D U(1) gauge theory with exact solutions.

Established equivalence between open and periodic boundary conditions in 2D case.

Explored initial steps for applying the technique to SU(2) lattice gauge theory.

Abstract

We discuss a new density of states (DoS) approach to solve the complex action problem that is caused by topological terms. The key ingredient is to use open boundary conditions for (at least) one of the directions, such that the quantization of the topological charge is lifted and the density becomes a regular function. We employ the DoS FFA method and compute the density of states as a function of the topological charge. Subsequent integration with suitable factors gives rise to the observables we are interested in. We here explore two test cases: U(1) lattice gauge theory in two dimensions, and SU(2) lattice gauge theory in four dimensions. Since the 2-d case has an exact solution we may use it to assess the method, in particular to establish the equivalence of the open boundary results with the usual choice of periodic boundary conditions. The SU(2) case is a first step of developing the techniques towards their eventual application in full QCD.