Hamiltonians and gaugeinvariant Hilbert space for lattice YangMillslike theories with finite gauge group
Abstract
Motivated by quantum simulation, we consider lattice Hamiltonians for YangMills 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 nonAbelian group, and derive some consequences from this fact. Independently of the chosen Hamiltonian, we provide a full explicit description of the physical, gaugeinvariant Hilbert space for pure gauge theories and derive a simple formula to compute its dimension. We illustrate the use of the gaugeinvariant basis to diagonalize a dihedral gauge theory on a small periodic lattice.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.12224
 arXiv:
 arXiv:2301.12224
 Bibcode:
 2023arXiv230112224M
 Keywords:

 Quantum Physics;
 High Energy Physics  Lattice
 EPrint:
 28 pages, 10 figures