The entanglement membrane in exactly solvable lattice models
arXiv:2312.12509 · doi:10.1103/PhysRevResearch.6.033271
Abstract
Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a non-trivial form that gives rise to a hierarchy of velocity scales with . For the lowest level of the hierarchy, circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop new methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform non-trivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits.
arXiv comment22 pages, 13 figures, 2 tables + 6 pages, 1 figure appendix; Added material: pedagogical introduction to entanglement membrane theory, extended bounds on in higher levels of the hierarchy, constructions of generalized dual-unitary gates based on complex Hadamard matrices, tensor product constructions
References in corpus (71)
- Quantum Computing in the NISQ era and beyond
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Quantum Simulation
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Black holes and the butterfly effect
- Black holes as mirrors: quantum information in random subsystems
- The ITensor Software Library for Tensor Network Calculations
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Time Evolution of Entanglement Entropy from Black Hole Interiors
- Operator Spreading in Random Unitary Circuits
- Chaos in quantum channels
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Random Quantum Circuits
- Entanglement Tsunami: Universal Scaling in Holographic Thermalization
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Information Scrambling in Computationally Complex Quantum Circuits
- Entanglement of Quantum Evolutions
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Emergent statistical mechanics of entanglement in random unitary circuits
- Absolute Maximal Entanglement and Quantum Secret Sharing
- Exact dynamics in dual-unitary quantum circuits
- Statistical mechanics of quantum error correcting codes
- Entanglement growth during thermalization in holographic systems
- On entanglement spreading in chaotic systems
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Unitary circuits of finite depth and infinite width from quantum channels
- Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
- The entanglement membrane in chaotic many-body systems
- Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Scrambling in Random Unitary Circuits: Exact Results
- Exact emergent quantum state designs from quantum chaotic dynamics
- Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
- Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
- Probing scrambling using statistical correlations between randomized measurements
- Maximum velocity quantum circuits
- Influence matrix approach to many-body Floquet dynamics
- Creating ensembles of dual unitary and maximally entangling quantum evolutions
- Temporal entanglement, quasiparticles and the role of interactions
- Optimal conversion of non--local unitary operations
- Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
- Membrane theory of entanglement dynamics from holography
- Computational power of one- and two-dimensional dual-unitary quantum circuits
- On entanglement spreading from holography
- Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
- Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
- Entanglement Tsunami in (1+1)-Dimensions
- Maximal entanglement velocity implies dual unitarity
- Exact local correlations in kicked chains at light cone edges
- Temporal Entanglement in Chaotic Quantum Circuits
- Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
- Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models
- Can local dynamics enhance entangling power?
- From Dual Unitarity to Generic Quantum Operator Spreading
- Hierarchical generalization of dual unitarity
- Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
- Nonlocal and controlled unitary operators of Schmidt rank three
- Exploring the Membrane Theory of Entanglement Dynamics
- Exact quench dynamics of the Floquet quantum East model at the deterministic point
- Exact Spectral Statistics in Strongly Localised Circuits
- Entanglement Growth and Minimal Membranes in Random Unitary Circuits
- Quantum information spreading in generalised dual-unitary circuits
- All unitaries having operator Schmidt rank 2 are controlled unitaries
- Real-time correlators in chaotic quantum many-body systems
- Zero-temperature entanglement membranes in quantum circuits
- Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
- Restrictions on the Schmidt rank of bipartite unitary operators beyond dimension two
- Dual unitaries as maximizers of the distance to local product gates
- Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
Cited by in corpus (12)
- Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
- Operator dynamics and entanglement in space-time dual Hadamard lattices
- Exactly solvable many-body dynamics from space-time duality
- Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
- Fundamental charges for dual-unitary circuits
- Entanglement in dual unitary quantum circuits with impurities
- More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
- Solvable Quantum Circuits in Tree+1 Dimensions
- Geometric constructions of generalized dual-unitary circuits from biunitarity
- Entanglement dynamics from universal low-lying modes
- Roughening Transition in Quantum Circuits
- Entanglement structure for finite system under dual-unitary dynamics