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, nonunique Laplacian operator on the finite Abelian or non-Abelian group and derive some consequences from this fact. Independent 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.

Mariani A., Pradhan S., Ercolessi E. (2023). Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group. PHYSICAL REVIEW D, 107(11), 1-15 [10.1103/PhysRevD.107.114513].

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

Pradhan S.;Ercolessi E.
Ultimo
2023

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, nonunique Laplacian operator on the finite Abelian or non-Abelian group and derive some consequences from this fact. Independent 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.
2023
Mariani A., Pradhan S., Ercolessi E. (2023). Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group. PHYSICAL REVIEW D, 107(11), 1-15 [10.1103/PhysRevD.107.114513].
Mariani A.; Pradhan S.; Ercolessi E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/962845
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