Spectrum-Generating Algebra in Higher Dimensional Gauge Theories

TL;DR

This paper demonstrates an approximate spectrum-generating algebra in a gauge theory model, predicting and verifying Quantum Many-Body Scars, and proposes observables for quantum simulation diagnostics.

Contribution

It introduces an approximate spectrum-generating algebra in higher-dimensional gauge theories and connects it to Quantum Many-Body Scars in spin-1 Quantum Link Models.

Findings

Existence of an approximate spectrum-generating algebra in a gauge theory model.

Prediction and verification of Quantum Many-Body Scars.

Proposal of observables for diagnosing the algebra in quantum simulators.

Abstract

Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.