Maximally Entangled Mode, Metal-Insulator Transition and Violation of Entanglement Area Law in Non-interacting Fermion Ground States

Abstract

We study in this work the ground state entanglement properties of two models of non-interacting fermions moving in one-dimension (1D), that exhibit metal-insulator transitions. We find that entanglement entropy grows either logarithmically or in a power-law fashion in the metallic phase, thus violating the (1D version of) entanglement area law. No such violation is found in the insulating phase. We further find that characteristics of {\em single fermion} states at the Fermi energy (which can {\em not} be obtained from the many-fermion Slater determinant) is captured by the lowest energy single fermion mode of the {\em entanglement} Hamiltonian; this is particularly true at the metal-insulator transition point. Our results suggest entanglement is a powerful way to detect metal-insulator transitions, {\em without} knowledge of the Hamiltonian of the system.

5 pages, 5 figures, a few references added

References in corpus (10)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Entanglement entropy and multifractality at localization transitions
• Replacing energy by von Neumann entropy in quantum phase transitions
• Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition
• Block Entanglement Entropy of Ground States with Long-Range Magnetic Order

Cited by in corpus (29)

• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Entanglement contour perspective for strong area law violation in a disordered long-range hopping model
• Entanglement spectrum and entangled modes of highly excited states in random XX spin chains
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• How much delocalisation is needed for an enhanced area law of the entanglement entropy?
• Entanglement and thermodynamic entropy in a clean many-body-localized system
• Anderson localization and momentum-space entanglement
• Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions
• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• Effect of Single Impurity on Free Fermion Entanglement Entropy
• Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
• Entanglement of Free Fermions and Bosons at Finite Temperature
• Entanglement entropy of XX spin $1/2$ chain with random partitioning at arbitrary temperature
• Testing the validity of random-singlet state for long-range hopping models through the scaling of entanglement entropy
• Quantum simulation of long range $XY$ quantum spin glass with strong area-law violation using trapped ions
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model