A new basis for Hamiltonian SU(2) simulations

TL;DR

This paper introduces a novel basis for simulating SU(2) lattice gauge theories in Hamiltonian form, improving efficiency across all coupling regimes and aiding quantum computing applications.

Contribution

It develops a new basis that preserves eigenvalues of the Hamiltonian at all couplings, enhancing simulation accuracy and applicability.

Findings

Eigenvalues of magnetic and electric Hamiltonians are preserved.

The basis is effective across all coupling strengths.

Provides an accessible introduction to Hamiltonian lattice gauge theories.

Abstract

Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely-used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories.