Coherence generation, symmetry algebras and Hilbert space fragmentation
arXiv:2212.14408 · doi:10.1103/PhysRevA.107.062402
Abstract
Hilbert space fragmentation is a novel type of ergodicity breaking in closed quantum systems. Recently, an algebraic approach was utilized to provide a definition of Hilbert space fragmentation characterizing \emph{families} of Hamiltonian systems based on their (generalized) symmetries. In this paper, we reveal a simple connection between the aforementioned classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP). The maximum CGP (in the basis associated to the algebra of each family of Hamiltonians) is exactly related to the number of independent Krylov subspaces , which is precisely the characteristic used in the classification of the system. In order to gain further insight, we numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension. More generally, allowing the time evolution to be any unitary channel in a specified algebra, we show analytically that the scaling of the Haar averaged value of the CGP depends only on . These results illustrate the intuitive relationship between coherence generation and symmetry algebras.
arXiv commentAccepted version, PRA, 5+3 pages
References in corpus (74)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Probing many-body dynamics on a 51-atom quantum simulator
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Decoherence Free Subspaces for Quantum Computation
- Noiseless Quantum Codes
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum many-body scars
- Many-body localization in a quantum simulator with programmable random disorder
- A Theory of Quantum Error-Correcting Codes
- Localization from Hilbert space shattering: from theory to physical realizations
- Local constraints can globally shatter Hilbert space: a new route to quantum information protection
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
- Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
- Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
- Exact Excited States of Non-Integrable Models
- Finite-size scaling of eigenstate thermalization
- Hilbert Space Fragmentation and Commutant Algebras
- Hilbert-Space Fragmentation from Strict Confinement
- Quantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals
- Unified structure for exact towers of scar states in the AKLT and other models
- Eigenstate thermalization within isolated spin-chain systems
- Statistical localization: from strong fragmentation to strong edge modes
- Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Quantum chaos and thermalization in gapped systems
- Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization
- Many Body Scars as a Group Invariant Sector of Hilbert Space
- Eta-pairing states as true scars in an extended Hubbard Model
- Error Avoiding Quantum Codes
- Dissipation and Decoherence in a Quantum Register
- Quantum scars from zero modes in an Abelian lattice gauge theory on ladders
- Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration
- Large Classes of Quantum Scarred Hamiltonians from Matrix Product States
- Exact three-colored quantum scars from geometric frustration
- The isolated Heisenberg magnet as a quantum time crystal
- Dynamical scar states in driven fracton systems
- From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras
- Quantum Many-Body Scar States in Two-Dimensional Rydberg Atom Arrays
- Topological many-body scar states in dimensions 1, 2, and 3
- Enlarged symmetry algebras of spin chains, loop models, and S-matrices
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Quaternion, harmonic oscillator, and high-dimensional topological states
- Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model
- Quasi-symmetry groups and many-body scar dynamics
- Disorder-free localization in an interacting two-dimensional lattice gauge theory
- A proposal for realising quantum scars in the tilted 1D Fermi-Hubbard model
- Quantum scars of bosons with correlated hopping
- Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains
- Coherence generating power of quantum unitary maps and beyond
- Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
- Many-body localization in a fragmented Hilbert space
- Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?
- Frustration-induced emergent Hilbert space fragmentation
- Measures of coherence generating power for quantum unital operations
- Nonergodic Quantum Dynamics from Deformations of Classical Cellular Automata
- Quantum Information Scrambling in Quantum Many-body Scarred Systems
- Disorder-free localization in a simple lattice gauge theory
- Scrambling of Algebras in Open Quantum Systems
- Coherence generating power of quantum dephasing processes
- The approach to typicality in many-body quantum systems
- Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
- Quantum scrambling of observable algebras
- Total correlations of the diagonal ensemble as a generic indicator for ergodicity breaking in quantum systems
- Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian Geometry
- Quantum information scrambling in the presence of weak and strong thermalization
- The frustration-free fully packed loop model
Cited by in corpus (5)
- Numerical Methods for Detecting Symmetries and Commutant Algebras
- Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
- Opening Krylov space to access all-time dynamics via dynamical symmetries
- Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies
- Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo