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

• URL: http://arxiv.org/abs/2412.09691v1
• Date: Thu, 12 Dec 2024 19:13:05 GMT
• Title: Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in $(2+1)$-D
• Authors: Graham Van Goffrier, Debasish Banerjee, Bipasha Chakraborty, Emilie Huffman, Sandip Maiti,
• Abstract summary: Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. We extend the model to $(2+1)d$ dimensions for the first time, and report on our initial results.
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• 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.

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