Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in $(2+1)$-D

TL;DR

This paper extends the study of $SO(3)$ quantum link models coupled with fermions from 1+1 dimensions to 2+1 dimensions, exploring their phase diagram and revealing complex phenomena like confinement and symmetry breaking.

Contribution

It introduces the first analysis of the $SO(3)$ quantum link model with fermions in 2+1 dimensions, including construction of gauge-invariant states and initial phase diagram insights.

Findings

Indications of a rich phase diagram with multiple phases.

Evidence of spontaneous and explicit chiral symmetry breaking.

Presence of confinement and magnetic phases.

Abstract

Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant subspace embedded onto local spin Hamiltonians for efficient quantum simulation. In $(1+1)d$ previous studies of the $SO(3)$ QLM coupled to adjoint fermionic matter have been shown to reflect key properties of QCD and nuclear physics, including distinct confining/deconfining phases and hadronic bound states. We extend the model to $(2+1)d$ dimensions for the first time, and report on our initial results. We review the construction of gauge-invariant state space for the proposed models, and study the single-plaquette ground state via exact-diagonalisation. We provide indications of a rich phase diagram which shows both spontaneous and explicit chiral symmetry breaking, confinement, and distinct magnetic phases characterised by different plaquette expectation values.