Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations

• URL: http://arxiv.org/abs/2311.11928v2
• Date: Wed, 17 Jul 2024 18:47:09 GMT
• Title: Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations
• Authors: Simone Romiti, Carsten Urbach,
• Abstract summary: We present a digitization scheme for the lattice $mathrmSU(2)$ gauge theory Hamiltonian in the $mathitmagnetic$ $mathitbasis$, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $mathrmSU(2)$ group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a digitization scheme for the lattice $\mathrm{SU}(2)$ gauge theory Hamiltonian in the $\mathit{magnetic}$ $\mathit{basis}$, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $\mathrm{SU}(2)$ group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning. This construction, analogous to a discrete Fourier transform, preserves the spectrum of the kinetic part of the Hamiltonian and the canonical commutation relations exactly on a subspace of the truncated Hilbert space, while the residual subspace can be projected above the cutoff of the theory.

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