Unusual area-law violation in random inhomogeneous systems

Abstract

The discovery of novel entanglement patterns in quantum many-body systems is a prominent research direction in contemporary physics. Here we provide the example of a spin chain with random and inhomogeneous couplings that in the ground state exhibits a very unusual area law violation. In the clean limit, i.e., without disorder, the model is the rainbow chain and has volume law entanglement. We show that, in the presence of disorder, the entanglement entropy exhibits a power-law growth with the subsystem size, with an exponent 1/2. By employing the Strong Disorder Renormalization Group (SDRG) framework, we show that this exponent is related to the survival probability of certain random walks. The ground state of the model exhibits extended regions of short-range singlets (that we term ``bubble'' regions) as well as rare long range singlet (``rainbow'' regions). Crucially, while the probability of extended rainbow regions decays exponentially with their size, that of the bubble regions is power law. We provide strong numerical evidence for the correctness of SDRG results by exploiting the free-fermion solution of the model. Finally, we investigate the role of interactions by considering the random inhomogeneous XXZ spin chain. Within the SDRG framework and in the strong inhomogeneous limit, we show that the above area-law violation takes place only at the free-fermion point of phase diagram. This point divides two extended regions, which exhibit volume-law and area-law entanglement, respectively.

arXiv comment28 pages, 19 figures

References in corpus (77)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Calculation of reduced density matrices from correlation functions
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Canonical Typicality
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Violation of the entropic area law for Fermions
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Strong disorder RG approach of random systems
• Aspects of generic entanglement
• Many-body localization in one dimension as a dynamical renormalization group fixed point
• Entanglement entropy of random quantum critical points in one dimension
• Density-Matrix Spectra of Solvable Fermionic Systems
• Entanglement dynamics after quantum quenches in generic integrable systems
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Entanglement of low-energy excitations in Conformal Field Theory
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Entanglement entropy of excited states
• Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records
• Power law violation of the area law in quantum spin chains
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• Criticality without frustration for quantum spin-1 chains
• The entanglement negativity in random spin chains
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Strong Disorder RG approach - a short review of recent developments
• Criticality and entanglement in random quantum systems
• Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Entanglement entropy dynamics of disordered quantum spin chains
• Density Matrices for a Chain of Oscillators
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Entanglement spectrum of random-singlet quantum critical points
• Precise Asymptotics for a Random Walker's Maximum
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Entanglement entropies in free fermion gases for arbitrary dimension
• Universal differential calculus on ternary algebras
• Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations
• Entanglement of excited states in critical spin chians
• Entanglement entropy of aperiodic quantum spin chains
• Entanglement vs. gap for one-dimensional spin systems
• Correlation amplitude and entanglement entropy in random spin chains
• Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain
• Volume Law for the Entanglement Entropy in Non-local QFTs
• Entanglement Entropies in Conformal Systems with Boundaries
• Deformed Fredkin Spin Chain with Extensive Entanglement
• Entanglement entropy of highly degenerate states and fractal dimensions
• Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains
• Increasing of entanglement entropy from pure to random quantum critical chains
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• A contour for the entanglement entropies in harmonic lattices
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Random transverse-field Ising chain with long-range interactions
• Ground State Entanglement in One Dimensional Translationally Invariant Quantum Systems
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Universal logarithmic terms in the entanglement entropy of 2d, 3d and 4d random transverse-field Ising models
• Protecting clean critical points by local disorder correlations
• Entanglement properties of correlated random spin chains and similarities with conformal invariant systems
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains
• Finite-size Gap, Magnetization, and Entanglement of Deformed Fredkin Spin Chain
• Entanglement in correlated random spin chains, RNA folding and kinetic roughening
• Area law violations in a supersymmetric model
• Entanglement Entropy from the Truncated Conformal Space
• Renyi entropy of highly entangled spin chains
• On the sharpness of the zero-entropy-density conjecture
• The gap of the area-weighted Motzkin spin chain is exponentially small
• The gap of Fredkin quantum spin chain is polynomially small
• Entanglement between random and clean quantum spin chains
• Entanglement across extended random defects in the XX spin chain

Cited by in corpus (31)

• Entanglement equipartition in critical random spin chains
• Strong Disorder RG approach - a short review of recent developments
• Holographic entanglement contour, bit threads, and the entanglement tsunami
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• Entanglement as geometry and flow
• Balanced Partial Entanglement and Mixed State Correlations
• Negativity Spectrum in the Random Singlet Phase
• Central charges of aperiodic holographic tensor network models
• Entanglement entropy from entanglement contour: higher dimensions
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Formulas for Partial Entanglement Entropy
• Quantum information geometry of driven CFTs
• Holographic rainbow networks for colorful Motzkin and Fredkin spin chains
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Casimir forces on deformed fermionic chains
• Link representation of the entanglement entropies for all bipartitions
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Entanglement entropy of the long-range Dyson hierarchical model
• Symmetry protected phases in inhomogeneous spin chains
• Sublogarithmic behaviour of the entanglement entropy in fermionic chains
• Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions
• Entanglement in non-critical inhomogeneous quantum chains
• Entanglement entropy and localization in disordered quantum chains
• Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line
• First Law and Quantum Correction for Holographic Entanglement Contour
• Entanglement-informed Construction of Variational Quantum Circuits
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Emergent geometry from entanglement structure