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

Abstract

We present a digitization scheme for the lattice $\mathrm{SU}(2)$ gauge theory Hamiltonian in the $magnetic$ $basis$, 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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Cited by in corpus (3)

• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Dynamics in Hamiltonian Lattice Gauge Theory: Approaching the Continuum Limit with Partitionings of SU$(2)$