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

Author:

Simone Romiti, Carsten Urbach

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), Quantum Physics (quant-ph)

journal:

date:

2023-11-20 00:00:00

Abstract

We present a digitization scheme for the lattice \(\mathrm{SU}(2)\) gauge theory Hamiltonian in the \emph{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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