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.
Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group / Mariani A.; Pradhan S.; Ercolessi E.. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - STAMPA. - 107:11(2023), pp. 114513.1-114513.15. [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.File | Dimensione | Formato | |
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