Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model

TL;DR

This paper develops new worldline and Kramers-Wannier dual representations of the SU(2) principal chiral model on the lattice, enabling Monte Carlo simulations at finite density by overcoming complex action issues.

Contribution

It introduces a novel worldline representation and a dual Kramers-Wannier form for the SU(2) model, facilitating simulations with finite chemical potential.

Findings

Successful derivation of real, positive weight worldline representation.

Implementation of dual variables satisfying constraints automatically.

Preliminary Monte Carlo results validating the dual approaches.

Abstract

In this letter we explore different representations of the SU(2) principal chiral model on the lattice. We couple chemical potentials to two of the conserved charges to induce finite density. This leads to a complex action such that the conventional field representation cannot be used for a Monte Carlo simulation. Using the recently developed Abelian color flux approach we derive a new worldline representation where the partition sum has only real and positive weights, such that a Monte Carlo simulation is possible. In a second step we transform the model to new dual variables in the Kramers-Wannier (KW) sense, such that the constraints are automatically fulfilled, and we obtain a second representation free of the complex action problem. We implement exploratory Monte Carlo simulations for both, the worldline, as well as the KW-dual form, for cross-checking the two dualizations and a first assessment of their potential for dual simulations.