Spontaneous Symmetry Breakings in $Z_2$ Gauge Theories for Doped Quantum Dimer and Eight-Vertex Models

TL;DR

This paper investigates how doped fermions in $Z_2$ gauge theories for quantum dimer and eight-vertex models exhibit spontaneous symmetry breaking, leading to superconducting or antiferromagnetic states depending on the phase, revealing complex interplay between fermions and background configurations.

Contribution

It demonstrates the spontaneous symmetry breaking of internal symmetries in doped fermions within $Z_2$ gauge theories, linking phase transitions to changes in background states in quantum dimer and eight-vertex models.

Findings

In the confinement phase, symmetries are spontaneously broken, resulting in superconducting or Neél states.

In the deconfinement phase, all symmetries are preserved.

Quantum phase transitions involve changes in both fermion and background groundstates.

Abstract

Behavior of doped fermions in $Z_2$ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the $Z_2$ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Ne\'el state appears. On the other hand in the deconfinement-topologically-ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped-fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.