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

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.

arXiv commentComments and a new plot for the relative errors added. Version to appear in Physics Letters B

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• Few-body physics on a space-time lattice in the worldline approach
• Tensor renormalization group approach to (1+1)-dimensional SU(2) principal chiral model at finite density
• Direct computational approach to lattice supersymmetric quantum mechanics
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