Vacuum Structure of the Ichimatsu-Decomposed Lattice Models

TL;DR

This paper investigates the vacuum structures of Ichimatsu-decomposed lattice gauge theories with fermionic symmetries, revealing phase diagrams with multiple phases in Z2 models and a single phase in SU(2) models.

Contribution

It introduces an Ichimatsu-decomposed lattice gauge theory framework and analyzes its vacuum phase structure using mean-field and numerical methods.

Findings

Two phases identified in 3D Z2 model

Single phase in 4D SU(2) model

Phase diagrams depend on coupling constants

Abstract

We proposed an `Ichimatsu'-decomposed lattice gauge theory with fermionic symmetries. The vacuum structures of the gauge sector with two coupling constants ($\beta_p,\beta_c$) are investigated for 3-dimensional Z$_2$ and 4-dimensional SU(2) cases using mean-field approximation and numerical simulation. We found two phases on the ($\beta_p,\beta_c$) phase diagram for 3-dim. Z$_2$ case, while the diagram is a single phase for the latter.