Year: 2024
Type: article
Abstract: 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 this for conventional symmetries such as Z 2 , U ( 1 ) , and S U ( 2 ) , where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. 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 hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of U ( 1 ) symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality. Published by the American Physical Society 2024
Source: PRX Quantum
Authors: Sanjay Moudgalya, Olexei I. Motrunich
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,450
Awards: G2229954460, G2403330605, G2432923657, G2595738051, G2958415499, The Institute for Quantum Information and Matter: Advancing the Entanglement Frontier, Exotic Quantum Criticalities in Low Dimensions and Systems with Unusual Quantum Many-Body Thermalization, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics, G961819192
OpenAlex ID: W4404757818