Density of states approach for lattice gauge theory with a $\theta$-term

Abstract

We discuss a new strategy for treating the complex action problem of lattice field theories with a $\theta$-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is not quantized to integers and the density of states is sufficiently well behaved such that it can be computed precisely with recently developed DoS techniques. After a general discussion of the approach and the role of the boundary conditions, we analyze the method for 2-d U(1) lattice gauge theory with a $\theta$-term, a model that can be solved in closed form. We show that in the continuum limit periodic and open boundary conditions describe the same physics and derive the DoS, demonstrating that only for open boundary conditions the density is sufficiently well behaved for a numerical evaluation. We conclude our proof of principle analysis with a small test simulation where we numerically compute the density and compare it with the analytical result.

arXiv commentReference added; slight change of title. Final version to appear in Nuclear Physics B

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• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations