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TT: Fachverband Tiefe Temperaturen
TT 71: Many-Body Quantum Dynamics I (joint session DY/TT)
TT 71.7: Talk
Thursday, March 21, 2024, 11:00–11:15, A 151
Symmetries as Ground States of Local Operators — •Sanjay Moudgalya1, 2 and Olexei Motrunich3 — 1Technical University of Munich, 85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany — 3Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a ``super-Hamiltonian". We demonstrate that for conventional on-site unitary symmetries, the symmetry algebras map to various kinds of ferromagnetic ground states. We obtain a physical interpretation of this super-Hamiltonian as the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits, which relates its low-energy excitations to approximate symmetries that determine slowly relaxing modes in symmetric systems. We find examples of gapped/gapless super-Hamiltonians indicating the absence/presence of slow-modes, which happens in the presence of discrete/continuous symmetries. In the gapless cases, we recover slow-modes such as diffusion in the presence of U(1) symmetry. We also demonstrate this framework for unconventional symmetries that lead to Hilbert space fragmentation and quantum many-body scars, which lead to novel kinds of slow-modes such as tracer diffusion and asymptotic quantum scars.
Keywords: Symmetry; Commutant Algebra; Random Circuits; Hilbert Space Fragmentation; Quantum Many-Body Scars