New developments for dual methods in lattice field theory at non-zero density

TL;DR

This paper discusses recent advances in dual variable methods for lattice field theory at finite density, demonstrating how they overcome the complex action problem and exploring their applications and limitations.

Contribution

It introduces dual variable mappings for the U(1) gauge Higgs system, discusses algorithmic and conceptual challenges, and explores partial dualization strategies for finite density lattice theories.

Findings

Dual variables successfully solve the complex action problem for certain models.

Representative physics results are obtained for the U(1) gauge Higgs system.

Partial dualization offers a promising approach in specific parameter regimes.

Abstract

In recent years the complex action problem of lattice field theory at finite density was overcome for several system by mapping them to dual variables (flux lines and surfaces). We illustrate this mapping for the case of the U(1) gauge Higgs system and present some representative physics results for this model. Conceptual challenges such as spectroscopy in the dual approach, as well as algorithmic developments are discussed and related ideas for systems with fermions are addressed. Models where the dual variables approach solves the complex action problem can serve as reference systems for other approaches to finite density lattice field theory and we discuss some examples. Finally we address the strategy of a partial dualization in certain limits, e.g., for strong coupling and large mass.