The sign problem and Abelian lattice duality

TL;DR

This paper demonstrates how duality transformations can convert complex-action Abelian lattice models with sign problems into real-action models, enabling more effective analysis and simulation across various parameter regions.

Contribution

It provides explicit duality relations for models with Z(N) and U(1) symmetries, generalizing known models and revealing new spatially-modulated phases.

Findings

Duality maps complex models to real models, resolving sign problems.

Explicit duality relations for Z(N) and U(1) models are derived.

Discovery of rich spatially-modulated phases in strong-coupling regions.

Abstract

For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.