Entanglement distribution in the Quantum Symmetric Simple Exclusion Process

Abstract

We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of $M$ particles, and focus on the late-time distribution of Rényi-$q$ entropies for a subsystem of size $\ell$. By means of a Coulomb gas approach from Random Matrix Theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For $q>1$, we show that, depending on the value of the ratio $\ell /M$, the entropy distribution displays either two or three distinct regimes, ranging from low- to high-entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.

arXiv comment6 pages, 3 figures; v2: minor revision

References in corpus (60)

• Entanglement in quantum critical phenomena
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Macroscopic fluctuation theory
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Solution of a minimal model for many-body quantum chaos
• Emergent statistical mechanics of entanglement in random unitary circuits
• Macroscopic current fluctuations in stochastic lattice gases
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Unravelling the large deviation statistics of Markovian open quantum systems
• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Spectral statistics and many-body quantum chaos with conserved charge
• Sub-ballistic growth of Rényi entropies due to diffusion
• The entanglement membrane in chaotic many-body systems
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Statistical distribution of quantum entanglement for a random bipartite state
• Scrambling in Random Unitary Circuits: Exact Results
• Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• Phase transitions of bipartite entanglement
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Open Quantum Symmetric Simple Exclusion Process
• A Random Unitary Circuit Model for Black Hole Evaporation
• Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions
• Operator Dynamics in Brownian Quantum Circuit
• The Page Curve for Fermionic Gaussian States
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Localization with random time-periodic quantum circuits
• Entanglement production and information scrambling in a noisy spin system
• Entanglement growth in diffusive systems
• Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems
• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Distribution of bipartite entanglement for random pure states
• Mixing properties of stochastic quantum Hamiltonians
• Entanglement structure of current-driven diffusive fermion systems
• Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes
• Entropy-Driven Phase Transitions of Entanglement
• Duality and hidden equilibrium in transport models
• Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case
• Large deviation eigenvalue density for the soft edge Laguerre and Jacobi $\beta$-ensembles
• Entanglement entropy growth in stochastic conformal field theory and the KPZ class
• Entanglement statistics in Markovian open quantum systems: a matter of mutation and selection
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Duality in quantum transport models
• Phase diagram of bipartite entanglement

Cited by in corpus (35)

• Random Quantum Circuits
• The Page Curve for Fermionic Gaussian States
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Symmetry-resolved Page curves
• Generalized Deep Thermalization for Free Fermions
• Entangled multiplets and unusual spreading of quantum correlations in a continuously monitored tight-binding chain
• Dissipative quasi-particle picture for quadratic Markovian open quantum systems
• Exact description of quantum stochastic models as quantum resistors
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems
• Can the Macroscopic Fluctuation Theory be Quantized?
• Designs via Free Probability
• Tight-binding billiards
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Entanglement asymmetry dynamics in random quantum circuits
• Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process
• Entropy fluctuation formulas of fermionic Gaussian states
• Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
• The non-stabilizerness of fermionic Gaussian states
• Spacetime picture for entanglement generation in noisy fermion chains
• Semi-classical theory of quantum stochastic resistors
• Non-Abelian entanglement asymmetry in random states
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP
• Field theory for monitored Brownian SYK clusters
• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Entanglement dynamics and Page curves in random permutation circuits
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Entanglement dynamics from universal low-lying modes
• Entanglement capacity of fermionic Gaussian states
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Volume-law entanglement entropy of typical pure quantum states
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble