Abstract
We propose an explicit formulation of the physical subspace for a (1+1)-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.
Highlights
Gauge theories play a central role in our understanding of modern particle physics, with the standard model being one of the most prominent examples
We show how, starting from a color-neutral basis developed in Ref. [55], the gauge d.o.f. can be integrated out on a lattice with open boundary conditions (OBC)
In contrast to Monte Carlo methods, the matrix product states (MPS) approach allows for access to the entanglement entropy, and we can study the scaling of the von Neumann entanglement entropy in the ground state while approaching the continuum limit
Summary
Gauge theories play a central role in our understanding of modern particle physics, with the standard model being one of the most prominent examples. A different approach to the Hamiltonian lattice formulation explored during recent years is quantum simulation of gauge theories [6,9,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]. Where the gauge d.o.f. are replaced by discrete spins These truncated models do not necessarily correspond to the continuum theory in the limit of vanishing lattice spacing, or might not have a continuum limit at all [54]. As we show in the paragraph, restricting oneself to the physically relevant subspace of these color-neutral superpositions allows for significantly reducing these superfluous d.o.f
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