Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model

TL;DR

This study explores how Z3 symmetry influences the sign problem and phase transition behavior in three-dimensional Potts models, revealing that Z3 symmetry significantly alleviates the sign problem and affects the deconfinement transition line.

Contribution

The paper constructs new Z3-symmetric 3D Potts models with varying states and demonstrates how Z3 symmetry reduces the sign problem and alters phase transition lines compared to traditional models.

Findings

Z3 symmetry nearly cures the sign problem.

The deconfinement transition line's dependence on chemical potential increases with more states.

Z3 symmetry impacts the phase transition behavior in the models.

Abstract

We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $\mu-\kappa$ plane as the number of states increases, where $\mu$ $(\kappa)$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $\mu$-dependence with respect to increasing the number of states.