Entanglement signatures of a percolating quantum system

Abstract

Entanglement measures have emerged as one of the versatile probes to diagnose quantum phases and their transitions. Universal features in them expand their applicability to a range of systems, including those with quenched disorder. In this work, we show that when the underlying lattice has percolation disorder, free fermions at a finite density show interesting entanglement properties due to massively degenerate ground states. We define and calculate appropriate entanglement measures such as typical, annealed, and quenched entanglement entropy in both one and two dimensions, showing they can capture both geometrical aspects and electronic correlations of the percolated quantum system. In particular, while typical and annealed entanglement show volume law character directly dependent on the number of zero modes in the system, quenched entanglement is generally area law albeit showing characteristic signatures of the classical percolation transition. Our work presents an exotic interplay between the geometrical properties of a lattice and quantum entanglement in a many-body quantum system.

arXiv comment7+3 pages, 4+3 Figures

References in corpus (63)

• Quantum entanglement
• A computable measure of entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement Entropy and Quantum Field Theory
• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Detecting topological order in a ground state wave function
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Average Entropy of a Subsystem
• Entanglement in a simple quantum phase transition
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Calculation of reduced density matrices from correlation functions
• An Area Law for One Dimensional Quantum Systems
• Reduced density matrices and entanglement entropy in free lattice models
• Area laws in quantum systems: mutual information and correlations
• On the quantum, classical and total amount of correlations in a quantum state
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Probing entanglement in a many-body-localized system
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Violation of the entropic area law for Fermions
• Entanglement spectrum of topological insulators and superconductors
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Universal terms for the entanglement entropy in 2+1 dimensions
• On the von Neumann capacity of noisy quantum channels
• Entanglement Entropy and the Fermi Surface
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Characterization of separable states and entanglement witnesses
• Universality of corner entanglement in conformal field theories
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• Partial time-reversal transformation and entanglement negativity in fermionic systems
• Statistical distribution of quantum entanglement for a random bipartite state
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Twisted and untwisted negativity spectrum of free fermions
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Characterizing disordered fermion systems using the momentum-space entanglement spectrum
• Entanglement Typicality
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Topological phase transitions in glassy quantum matter
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Entanglement negativity between separated regions in quantum critical systems
• Dynamical Aspects of 2D Quantum Percolation
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• Detecting entanglement of random states with an entanglement witness
• Localization-delocalization transitions in a two-dimensional quantum percolation model: von Neumann entropy studies
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Localization phase diagram of two-dimensional quantum percolation
• Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
• Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids
• Inhibition of spread of typical bipartite and genuine multiparty entanglement in response to disorder
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Symmetry classification of typical quantum entanglement
• Percolation Transition in a Topological Phase