Entanglement Transitions from Holographic Random Tensor Networks

Abstract

We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the "holographic" boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

v2: 18 pages, 8 figures. Published version

References in corpus (18)

• The density-matrix renormalization group in the age of matrix product states
• Localization of interacting fermions at high temperature
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Black holes as mirrors: quantum information in random subsystems
• Many-body localization edge in the random-field Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Criticality, the area law, and the computational power of PEPS
• Unitary-projective entanglement dynamics
• Surface/State Correspondence as a Generalized Holography
• Quantum quenches in the many-body localized phase
• Analytically solvable renormalization group for the many-body localization transition
• Quantum revivals and many-body localization
• Consistency Conditions for an AdS/MERA Correspondence
• Spectral tensor networks for many-body localization
• Protection of topological order by symmetry and many-body localization
• Many-Body Localization of Symmetry Protected Topological States

Cited by in corpus (164)

• Measurement-driven entanglement transition in hybrid quantum circuits
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Random Quantum Circuits
• Critical properties of the measurement-induced transition in random quantum circuits
• Scalable probes of measurement-induced criticality
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Statistical mechanics of quantum error correcting codes
• Measurement Protected Quantum Phases
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Measurement-induced phase transition: A case study in the non-integrable model by density-matrix renormalization group calculations
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Efficient classical simulation of random shallow 2D quantum circuits
• Operator scaling dimensions and multifractality at measurement-induced transitions
• The entanglement membrane in chaotic many-body systems
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Scrambling in Random Unitary Circuits: Exact Results
• Topological order and criticality in (2+1)D monitored random quantum circuits
• Long-range entanglement from measuring symmetry-protected topological phases
• Entanglement Negativity at Measurement-Induced Criticality
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Mean-field entanglement transitions in random tree tensor networks
• Nonlinear sigma models for monitored dynamics of free fermions
• A Random Unitary Circuit Model for Black Hole Evaporation
• Entanglement entropy scaling transition under competing monitoring protocols
• Entanglement dynamics in hybrid quantum circuits
• Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Controlling entanglement at absorbing state phase transitions in random circuits
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Disordered monitored free fermions
• Entanglement transitions with free fermions
• Measurement-induced criticality as a data-structure transition
• Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
• Entanglement phase transitions in random stabilizer tensor networks
• Measurement-induced purification in large-N hybrid Brownian circuits
• Deep Learning and AdS/QCD
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Entanglement in one-dimensional critical state after measurements
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Purification Timescales in Monitored Fermions
• Triviality of quantum trajectories close to a directed percolation transition
• Yang-Lee edge singularity triggered entanglement transition
• Probing sign structure using measurement-induced entanglement
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
• Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution
• Measurement-induced phase transitions on dynamical quantum trees
• Non-Hermitian topology in monitored quantum circuits
• Finite-time teleportation phase transition in random quantum circuits
• Growth of entanglement of generic states under dual-unitary dynamics
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Entanglement phase transitions in non-Hermitian quasicrystals
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Measurement induced entanglement transition in two dimensional shallow circuit
• Neural ODE and Holographic QCD
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Infinite-randomness criticality in monitored quantum dynamics with static disorder
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Toward random tensor networks and holographic codes in CFT
• Negativity Spectra in Random Tensor Networks and Holography
• Random tensor networks with nontrivial links
• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Entanglement dynamics in the many-body Hatano-Nelson model
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Localization as an entanglement phase transition in boundary-driven Anderson models
• Evolution of many-body systems under ancilla quantum measurements
• Diagnosis of information scrambling from Hamiltonian evolution under decoherence
• Absence of measurement-induced entanglement transition due to feedback-induced skin effect
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Hayden-Preskill decoding from noisy Hawking radiation
• Stirring by Staring: Measurement Induced Chirality
• Boundary transfer matrix spectrum of measurement-induced transitions
• Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
• Field theory of monitored, interacting fermion dynamics with charge conservation
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain
• Renormalization group for measurement and entanglement phase transitions
• Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
• Entanglement Transitions in Unitary Circuit Games
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
• Entanglement and absorbing state transitions in $(d+1)$-dimensional stabilizer circuits
• Universal structure of measurement-induced information in many-body ground states
• A Dyson Brownian motion model for weak measurements in chaotic quantum systems
• Production of lattice gauge-Higgs topological states in measurement-only quantum circuit
• Purification and scrambling in a chaotic Hamiltonian dynamics with measurements
• Quantum simulation using noisy unitary circuits and measurements
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Quantum and Classical Dynamics with Random Permutation Circuits
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Steering-induced phase transition in measurement-only quantum circuits
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODE
• Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Unraveling superradiance: Entanglement and mutual information in collective decay
• Locally purified density operators for noisy quantum circuits
• Spacetime picture for entanglement generation in noisy fermion chains
• Sign problem in tensor network contraction
• Protect Measurement-Induced Phase Transition from Noise
• Random insights into the complexity of two-dimensional tensor network calculations
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Critical Properties of Weak Measurement Induced Phase Transitions in Random Quantum Circuits
• The Measurement-induced Transition in Long-range Interacting Quantum Circuits
• Designs from magic-augmented Clifford circuits
• Phase transition in von Neumann entanglement entropy from replica symmetry breaking
• Prolonging a discrete time crystal by quantum-classical feedback
• Entanglement phase transitions in non-Hermitian Kitaev chains
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Topological Modes in Monitored Quantum Dynamics
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Measurement-induced phase transitions in systems with diffusive dynamics
• Statistical Mechanics of Stochastic Quantum Control: $d$-adic Rényi Circuits
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Engineering holography with stabilizer graph codes
• Phase transitions induced by standard and predetermined measurements in transmon arrays
• Entanglement transitions from restricted Boltzmann machines
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Tensor product random matrix theory
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model
• Random Quantum Circuits with Time-Reversal Symmetry
• Concomitant Entanglement and Control Criticality Driven by Collective Measurements
• Emergence of Navier-Stokes hydrodynamics in chaotic quantum circuits
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Tensor Renormalization Group for interacting quantum fields
• Monitored Fluctuating Hydrodynamics
• Universality classes for purification in nonunitary quantum processes
• Elusive phase transition in the replica limit of monitored systems
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Symmetry and Topology of Monitored Quantum Dynamics
• Symmetric tensor scars with tunable entanglement from volume to area law
• Pseudoentanglement from tensor networks
• Measurement-Induced Entanglement in Conformal Field Theory
• Measurement-induced criticality in extended and long-range unitary circuits
• Plaquette Models, Cellular Automata, and Measurement-induced Criticality
• Field theory of charge sharpening in symmetric monitored quantum circuits
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Chiral symmetry breaking generalizes in tensor theories
• Universality in Non-Equilibrium Quantum Systems
• Highly entangled spin chains and 2D quantum gravity
• Roughening Transition in Quantum Circuits
• Engineering entanglement geometry via spacetime-modulated measurements
• Tri-unitary quantum circuits
• Holographic Tensor Networks as Tessellations of Geometry
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions