Scrambling and operator entanglement in local non-Hermitian quantum systems
arXiv:2305.12054 · doi:10.1103/PhysRevB.108.134305
Abstract
The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in non-Hermitian variants of paradigmatic local quantum spin-chain models. We utilize a mixture of exact diagonalization and tensor network techniques for our numerical results and focus on three dynamical quantities: (i) out-of-time-ordered correlators (OTOCs), (ii) operator entanglement of the dynamics, and (iii) entanglement growth following a quench from product initial states. We show that while OTOCs fail to capture information scrambling in a simple, local, non-Hermitian transverse-field Ising model, the closely related operator entanglement is a robust measure of dynamical properties of interest. Moreover, we show that the short-time growth of operator entanglement can generically detect ``entanglement phase transitions'' in these systems while its long-time average is shown to be a reliable indicator of quantum chaos and entanglement phases. This allows us to extend operator entanglement based diagnostics from previous works on closed and open quantum systems, to the new arena of monitored quantum dynamics. Finally, we remark on the efficacy of these dynamical quantities in detecting integrability/chaos in the presence of continuous monitoring.
arXiv comment16+6 pages, comments welcome; v2: additional references, figures, and appendix added; v3: close to published version. PRB Editors' Suggestion
References in corpus (106)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Many body localization and thermalization in quantum statistical mechanics
- Efficient classical simulation of slightly entangled quantum computations
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Random Matrix Theories in Quantum Physics: Common Concepts
- A Quantum Engineer's Guide to Superconducting Qubits
- Many-body localization, thermalization, and entanglement
- Complex Extension of Quantum Mechanics
- Non-Hermitian Physics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Symmetry and Topology in Non-Hermitian Physics
- Anomalous edge state in a non-Hermitian lattice
- The ITensor Software Library for Tensor Network Calculations
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Area laws in quantum systems: mutual information and correlations
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Chaos in quantum channels
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Lieb-Schultz-Mattis in Higher Dimensions
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Many-body localization: an introduction and selected topics
- Dynamics of Loschmidt echoes and fidelity decay
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Measurement-driven entanglement transition in hybrid quantum circuits
- Spectral Gap and Exponential Decay of Correlations
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Ballistic spreading of entanglement in a diffusive nonintegrable system
- Black Holes and Random Matrices
- Biorthogonal Quantum Mechanics
- Unitary-projective entanglement dynamics
- Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
- Dynamical purification phase transitions induced by quantum measurements
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Strong and weak thermalization of infinite non-integrable quantum systems
- Circuit QED lattices: towards quantum simulation with superconducting circuits
- Non-Hermitian Many-Body Localization
- Information Scrambling in Computationally Complex Quantum Circuits
- Out-of-Time-Order Correlation for Many-Body Localization
- Entanglement of Quantum Evolutions
- A simple model of quantum trajectories
- Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
- Entanglement dynamics after quantum quenches in generic integrable systems
- Exploring Localization in Nuclear Spin Chains
- Entanglement phase transitions in measurement-only dynamics
- Quantum quench dynamics
- Out-of-time-ordered correlators in many-body localized systems
- Operator space entanglement entropy in transverse Ising chain
- Introduction to Random Matrices - Theory and Practice
- Heralded magnetism in non-Hermitian atomic systems
- Loschmidt Echo
- Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- Directed Quantum Chaos
- Weak Quantum Chaos
- Entanglement and purification transitions in non-Hermitian quantum mechanics
- Entanglement and spin squeezing in non-Hermitian phase transitions
- Information Scrambling and Loschmidt Echo
- Random Matrices close to Hermitian or unitary: overview of methods and results
- Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators
- The quasiprobability behind the out-of-time-ordered correlator
- Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
- Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
- Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
- Measurement as a shortcut to long-range entangled quantum matter
- Probing quantum information propagation with out-of-time-ordered correlators
- Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
- Universality classes of non-Hermitian random matrices
- Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
- Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
- Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
- Operator Space Entanglement Entropy in XY Spin Chains
- Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
- Density Matrix Renormalization Group in the Heisenberg Picture
- Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
- Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
- Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
- Information Scrambling and Chaos in Open Quantum Systems
- Structure of chaotic eigenstates and their entanglement entropy
- A Multi-Dimensional Lieb-Schultz-Mattis Theorem
- Diffusion in a Random Velocity Field: Spectral Properties of a Non-Hermitian Fokker-Planck Operator
- Complexity of thermal states in quantum spin chains
- Universal eigenstate entanglement of chaotic local Hamiltonians
- Entangling power of time-evolution operators in integrable and nonintegrable many-body systems
- Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
- Detection of quantum phases via out-of-time-order correlators
- Exploring quantum signatures of chaos on a Floquet synthetic lattice
- Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
- Entropic uncertainty relations for quantum information scrambling
- Out-of-time-order correlations and Floquet dynamical quantum phase transition
- Detecting dynamical quantum phase transition via out-of-time-order correlations in a solid-state quantum simulator
- Quantum coherence as a signature of chaos
- Correlations at PT-symmetric quantum critical point
- Bipartite quantum systems: on the realignment criterion and beyond
- Can local dynamics enhance entangling power?
- Scrambling of Algebras in Open Quantum Systems
- Quantum scrambling of observable algebras
- Chaos and High Temperature Pure State Thermalization
- BROTOCs and Quantum Information Scrambling at Finite Temperature
- On the relation between Schmidt coefficients and entanglement
- Non-Hermitian chiral anomalies
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- Locality, Correlations, Information, and non-Hermitian Quantum Systems
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