Entanglement dynamics in the three-dimensional Anderson model

Abstract

We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $\sim \ln \ln t$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.

References in corpus (58)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• The many-body localization phase transition
• Time-dependence of correlation functions following a quantum quench
• Many-body localization edge in the random-field Heisenberg chain
• Unbounded growth of entanglement in models of many-body localization
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Reduced density matrices and entanglement entropy in free lattice models
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Probing entanglement entropy via randomized measurements
• Probing entanglement in a many-body-localized system
• Universal dynamics and renormalization in many body localized systems
• Quantum chaos challenges many-body localization
• Theory of the many-body localization transition in one dimensional systems
• The entanglement of indistinguishable particles shared between two parties
• Universal properties of many-body delocalization transitions
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Localization of bosonic atoms by fermionic impurities in a 3d optical lattice
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• Density-Matrix Spectra of Solvable Fermionic Systems
• Dynamical obstruction to localization in a disordered spin chain
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Entanglement from Charge Statistics: Exact Relations for Many-Body Systems
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Absence of true localization in many-body localized phases
• Symmetry resolved entanglement in free fermionic systems
• Delocalization Transition via Supersymmetry in one Dimension
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Quantum entanglement theory in the presence of superselection rules
• Entanglement of indistinguishable particles in condensed matter physics
• Nonlocal resources in the presence of Superselection Rules
• On the reduced density matrix for a chain of free electrons
• Purification and many-body localization in cold atomic gases
• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Many-body localization in infinite chains
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Is there slow particle transport in the MBL phase?
• Entanglement entropy dynamics of disordered quantum spin chains
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Operational Entanglement of Symmetry-Protected Topological Edge States
• Entanglement entropy and multifractality at localization transitions
• Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems
• Entanglement entropy of disordered quantum chains following a global quench
• Scaling of entanglement entropy and superselection rules
• Decay of density waves in coupled one-dimensional many-body-localized systems
• Logarithmic entanglement growth in two-dimensional disordered fermionic systems
• Localization of fermions in coupled chains with identical disorder

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• Symmetry resolved relative entropies and distances in conformal field theory
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• Scale-Invariant Survival Probability at Eigenstate Transitions
• Scale-invariant critical dynamics at eigenstate transitions
• Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
• Symmetry-resolved entanglement in fermionic systems with dissipation
• What can we learn from diffusion about Anderson localization of a degenerate Fermi gas?
• Speed limits to fluctuation dynamics
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
• Critical quantum dynamics of observables at eigenstate transitions
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models