Growth of entanglement of generic states under dual-unitary dynamics
arXiv:2208.00030 · doi:10.1103/PhysRevB.107.174311
Abstract
Dual-unitary circuits are a class of locally-interacting quantum many-body systems displaying unitary dynamics also when the roles of space and time are exchanged. These systems have recently emerged as a remarkable framework where certain features of many-body quantum chaos can be studied exactly. In particular, they admit a class of ``solvable" initial states for which, in the thermodynamic limit, one can access the full non-equilibrium dynamics. This reveals a surprising property: when a dual-unitary circuit is prepared in a solvable state the quantum entanglement between two complementary spatial regions grows at the maximal speed allowed by the local structure of the evolution. Here we investigate the fate of this property when the system is prepared in a generic pair-product state. We show that in this case the entanglement increment during a time step is sub-maximal for finite times, however, it approaches the maximal value in the infinite-time limit. This statement is proven rigorously for dual-unitary circuits generating high enough entanglement, while it is argued to hold for the entire class.
17 pages, 3 figures
References in corpus (37)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Many body localization and thermalization in quantum statistical mechanics
- Many body localization in Heisenberg XXZ magnet in a random field
- Entropy scaling and simulability by Matrix Product States
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- What is an integrable quench?
- Postselection-free entanglement dynamics via spacetime duality
- Maximally multipartite entangled states
- Genuinely multipartite entangled states and orthogonal arrays
- Scrambling in Random Unitary Circuits: Exact Results
- Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
- On entropy growth and the hardness of simulating time evolution
- Exact emergent quantum state designs from quantum chaotic dynamics
- Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
- Temporal entanglement, quasiparticles and the role of interactions
- Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
- Computational power of one- and two-dimensional dual-unitary quantum circuits
- Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
- Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
- Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
- Entanglement Barriers in Dual-Unitary Circuits
- Entanglement growth and simulation efficiency in one-dimensional quantum lattice systems
- Maximal entanglement velocity implies dual unitarity
- Construction and the ergodicity properties of dual unitary quantum circuits
- Scaling of temporal entanglement in proximity to integrability
- Global large time dynamics and the generalized Gibbs ensemble
- Exact dynamics in dual-unitary quantum circuits with projective measurements
- Many Body Quantum Chaos and Dual Unitarity Round-a-Face
- Many-Body Quantum Chaos and Space-time Translational Invariance
- Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
- Dual unitary circuits in random geometries
- Exact Spectral Statistics in Strongly Localised Circuits
- Ternary unitary quantum lattice models and circuits in dimensions
- Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
- Entanglement dynamics of thermofield double states in integrable models
- Tri-unitary quantum circuits
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- Temporal Entanglement in Chaotic Quantum Circuits
- Majorana Loop Models for Measurement-Only Quantum Circuits
- Quantum information spreading in generalised dual-unitary circuits
- Quantum Many-Body Scars in Dual-Unitary Circuits
- From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
- Exactly solvable many-body dynamics from space-time duality
- Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
- Operator dynamics and entanglement in space-time dual Hadamard lattices
- Quantum and Classical Dynamics with Random Permutation Circuits
- Two-step relaxation in local many-body Floquet systems
- Fundamental charges for dual-unitary circuits
- Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
- Exact results on the dynamics of the stochastic Floquet-East model
- Hopf algebras and solvable unitary circuits
- Structural Stability Hypothesis of Dual Unitary Quantum Chaos
- Entanglement in dual unitary quantum circuits with impurities
- Geometric constructions of generalized dual-unitary circuits from biunitarity
- Boundary Chaos: Spectral Form Factor
- Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
- Entanglement structure for finite system under dual-unitary dynamics