Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Spectrum-Generating Algebra in Higher Dimensional Gauge Theories
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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.
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An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
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Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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Hilbert Space Fragmentation and Gauge Symmetry
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.