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arXiv · 2301.12224

Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group

A. Mariani·S. Pradhan·E. Ercolessi
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Abstract

Motivated by quantum simulation, we consider lattice Hamiltonians for Yang-Mills gauge theories with finite gauge group, for example a finite subgroup of a compact Lie group. We show that the electric Hamiltonian admits an interpretation as a certain natural, non-unique Laplacian operator on the finite Abelian or non-Abelian group, and derive some consequences from this fact. Independently of the chosen Hamiltonian, we provide a full explicit description of the physical, gauge-invariant Hilbert space for pure gauge theories and derive a simple formula to compute its dimension. We illustrate the use of the gauge-invariant basis to diagonalize a dihedral gauge theory on a small periodic lattice.

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A. Mariani, S. Pradhan, E. Ercolessi. 2023-01-28. Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group. https://doi.org/10.1103/physrevd.107.114513

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