An Area Law for One Dimensional Quantum Systems

Abstract

We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on completely positive maps which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, the bound on Von Neumann entropy implies a bound on Rényi entropy for sufficiently large $\alpha <1$ and implies the ability to approximate the ground state by a matrix product state.

9 pages, 1 figure; typo fixed in Eq. 41; typo fixed in Eq. 4; note added

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• Matrix product state approach for a quantum system at finite temperatures using random phases and Trotter gates
• Entanglement front generated by an impurity travelling in an isolated many-body quantum system
• Localized Virtual Purification
• Bridging Entanglement and Magic Resources within Operator Space
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Tensor network methods with graph enhancement
• Pruning a restricted Boltzmann machine for quantum state reconstruction
• Quantum simulation using noisy unitary circuits and measurements
• Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems
• Purity of thermal mixed quantum states
• Weak ergodicity breaking in Josephson-junction arrays
• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension
• Approximating local properties by tensor network states with constant bond dimension
• Continuum limits of homogeneous binary trees and the Thompson group
• Entropy Constraints for Ground Energy Optimization
• Wilsonian Effective Action and Entanglement Entropy
• Connected components of irreducible maps and 1D quantum phases
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III
• More on symmetry resolved operator entanglement
• An entropy perspective on the thermal crossover in a fermionic Hubbard chain
• Entanglement phase diagrams from partial transpose moments
• Quantum ground state isoperimetric inequalities for the energy spectrum of local Hamiltonians
• Hybrid Tree Tensor Networks for quantum simulation
• Flat Bands and Compact Localised States: A Carrollian roadmap
• The pair-flip model: a very entangled translationally invariant spin chain
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States
• Infinite randomness with continuously varying critical exponents in the random XYZ spin chain
• Locally purified density operators for noisy quantum circuits
• Russian doll spectrum in a non-Abelian string-net ladder
• Quantitatively improved finite-size criteria for spectral gaps
• Identifying quantum phases from injectivity of symmetric matrix product states
• Maximal Speed of Propagation in Open Quantum Systems
• Quantum Hamiltonian complexity and the detectability lemma
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Rényi free energy and variational approximations to thermal states
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Asymptotically Decreasing Lieb-Robinson Velocity for a Class of Dissipative Quantum Dynamics
• Single-copy entanglement in a gapped quantum spin chain
• Unfolding quantum master equation into a system of real-valued equations: computationally effective expansion over the basis of $SU(N)$ generators
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Determining the structure of real-space entanglement spectrum from approximate conditional independence
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Local order parameters for symmetry fractionalization
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• Exact renormalization in quantum spin chains
• Random translation-invariant Hamiltonians and their spectral gaps
• Many-body entanglement and topology from uncertainties and measurement-induced modes
• Effect of long-range interactions on multipartite entanglement in Heisenberg chains
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• On ${\mathbb{Z}}_2$-indices for ground states of fermionic chains
• Splitting a critical spin chain
• Entropic topological invariant for a gapped one-dimensional system
• Thermal Area Law in Long-Range Interacting Systems
• Matrix Product Density Operators: when do they have a local parent Hamiltonian?
• Markovianity of an emitter coupled to a structured spin chain bath
• Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
• Matrix product state approach to a frustrated spin chain with long-range interactions
• Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Frustration-free Hamiltonians supporting Majorana zero edge modes
• Hilbert space renormalization for the many-electron problem
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
• Measuring energy by measuring any other observable
• Two rate periodic protocol with dynamics driven through many cycles
• Undecidability in Physics: a Review
• Universal Time-Entanglement Trade-off in Open Quantum Systems
• Dynamical simulations of carotenoid photoexcited states using density matrix renormalization group techniques
• The Schmidt rank for the commuting operator framework
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Introduction to quantum entanglement in many-body systems
• Quantum Compression of Tensor Network States
• Many-Body Localization: Concepts and Simple Models
• Deforming the Fredkin spin chain away from its frustration-free point
• Entanglement bounds in the XXZ quantum spin chain
• Finite-depth scaling of infinite quantum circuits for quantum critical points
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Measurement-Induced Spectral Transition
• Pivoting through the chiral-clock family
• Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems
• Matrix Product States with adaptive global symmetries
• Matrix product approximations to multipoint functions in two-dimensional conformal field theory
• Single-shot holographic compression from the area law
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• Measurement-induced entanglement transition in chaotic quantum Ising chain
• Markovian Matrix Product Density Operators : Efficient computation of global entropy
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension
• Two-dimensional local Hamiltonian problem with area laws is QMA-complete
• Universal Characterization of Quantum Many-Body States through Local Information
• An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
• TNSPackage: A Fortran2003 library designed for tensor network state methods
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• Composite symmetry protected topological order and effective models
• Multi-level, multi-party singlets as ground states and their role in entanglement distribution
• On Lieb-Robinson bounds for a class of continuum fermions
• Entropic relations for indistinguishable quantum particles
• Matrix product approximations to conformal field theories
• Efficiency of neural quantum states in light of the quantum geometric tensor
• A near-term quantum simulation of the transverse field Ising model hints at Glassy Dynamics
• Dual-isometric Projected Entangled Pair States
• Fourier-space entanglement of spin chains
• Locality estimes for complex time evolution in 1D
• On the spectral gap of random quantum channels
• Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking
• Inference from Matrix Products: A Heuristic Spin Glass Algorithm
• Circuit lower bounds for low-energy states of quantum code Hamiltonians
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Entanglement Dynamics between Ising Spins and a Central Ancilla
• Matrix-product unitaries: Beyond quantum cellular automata
• Fermionic logarithmic negativity in the Krawtchouk chain
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Tunable Geometries in Sparse Clifford Circuits
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Perturbative gadgets without strong interactions
• The Detectability Lemma and Quantum Gap Amplification
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries
• Thermal Area Law for Lattice Bosons
• Area laws and efficient descriptions of quantum many-body states
• Lieb-Robinson Bounds for the Toda Lattice
• Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
• Differentiable matrix product states for simulating variational quantum computational chemistry
• Efficient Quantum Circuits based on the Quantum Natural Gradient
• Universal noise-precision relations in variational quantum algorithms
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
• Single-layer tensor network approach for three-dimensional quantum systems
• The resource theory of tensor networks
• Renormalized entropy of entanglement in relativistic field theory
• Gauging quantum states with non-anomalous matrix product operator symmetries
• Entanglement of Valence-Bond-Solid on an Arbitrary Graph
• The continuum limit of a tensor network: a path integral representation
• DMRG studies on linear-exchange quantum spin models in one dimension
• Practical variational tomography for critical 1D systems
• Entanglement entropy from SU(2) Chern-Simons theory and symmetric webs
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• A Matrix Product State Model for Simultaneous Classification and Generation
• Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints
• Area laws and thermalization from classical entropies in a Bose-Einstein condensate
• Entanglement Fractalization
• Bicolor loop models and their long range entanglement
• Finite-Entanglement Scaling of 2D Metals
• Area law for steady states of detailed-balance local Lindbladians
• Boiling Quantum Vacuum: Thermal Subsystems from Ground-State Entanglement
• Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
• Novel quantum phases on graphs using abelian gauge theory
• Tensor networks and efficient descriptions of classical data
• Coarse-grained spectral projection (CGSP): a deep learning-assisted approach to quantum unitary dynamics
• Minimally entangled typical thermal states algorithm with Trotter gates
• A polynomial-time algorithm for ground states of spin trees
• Entanglement subvolume law for 2D frustration-free spin systems
• Time-Polynomial Lieb-Robinson bounds for finite-range spin-network models
• Pairwise Concurrence in Cyclically Symmetric Quantum States
• Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture
• Correlations in Quantum Spin Systems from the Boundary Effect
• Dispersive Estimates for Harmonic Oscillator Systems
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Symmetries and local transformations of translationally invariant Matrix Product States
• The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
• Area law and universality in the statistics of subsystem energy
• Tensor network non-zero testing
• Quantum nuclear dynamics on a distributed set of ion-trap quantum computing systems
• Enhanced Lieb-Robinson bounds for commuting long-range interactions
• Fractional domain wall statistics in spin chains with anomalous symmetries
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Approximation, Proof Systems, and Correlations in a Quantum World
• Entropy estimation in a spin-1 Bose-Einstein condensate
• Variational Microcanonical Estimator
• Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains
• Emergent random matrix universality in quantum operator dynamics
• Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
• From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Multipartite maximally entangled states in symmetric scenarios
• Adiabatic freezing of entanglement with insertion of defects in a one-dimensional Hubbard model
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Internal structure of gauge-invariant Projected Entangled Pair States
• Efficient simulation of many-body localized systems
• Time Evolution and Deterministic Optimisation of Correlator Product States
• Properties of thermal quantum states: locality of temperature, decay of correlations, and more
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Classification of the phases of 1D spin chains with commuting Hamiltonians
• $Q$-Deformed Rainbows: a Universal Simulator of Free Entanglement Spectra
• Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
• Anatomy of localisation protected quantum order on Hilbert space
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Low-Rank Approximability and Entropy Area Laws for Ground States of Unbounded Hamiltonians
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• On Hastings factorization for quantum many-body systems in the infinite volume setting
• Adiabatic ground state preparation in an expanding lattice
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Spatial distribution of superfluidity and superfluid distillation of Bose liquids
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Quantum lozenge tiling and entanglement phase transition
• Many-body localization in the droplet spectrum of the random XXZ quantum spin chain
• Classifying topological neural network quantum states via diffusion maps
• Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Exploiting many-body localization for scalable variational quantum simulation
• The Area Term of the Entanglement Entropy of a Supersymmetric $O(N)$ Vector Model in Three Dimensions
• Anomalous Enhancement of Entanglement Entropy in Nonequilibrium Steady States Driven by Zero-Temperature Reservoirs
• Towards a better understanding of the matrix product function approximation algorithm in application to quantum physics
• Diagonal entropy in many-body systems: Volume effect and quantum phase transitions
• Quantum Entanglement In Inhomogeneous 1D Systems
• Non-Interacting Motzkin Chain - Periodic Boundary Conditions
• Engineering large end-to-end correlations in finite fermionic chains
• Tensor Ring Decomposition: Optimization Landscape and One-loop Convergence of Alternating Least Squares
• Lieb-Robinson bounds imply locality of interactions
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
• Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
• Quantum max-flow in the bridge graph
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Classifying fermionic states via many-body correlation measures
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Sample complexity of matrix product states at finite temperature
• Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement
• Effects of Topological Boundary Conditions on Bell Nonlocality
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Tree-size complexity of multiqubit states
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Parent Lindbladians for Matrix Product Density Operators
• Lieb-Robinson bounds with exponential-in-volume tails
• Entanglement and private information in many-body thermal states
• Transitions of the Lyapunov spectrum and entanglement entropy in monitored quantum dynamics with homogeneous unitary gates
• Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Gauging Quantum Phases: A Matrix Product State Approach
• Boundedness of Entanglement Entropy,and Split Property of Quantum Spin Chains
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• The Software Landscape for the Density Matrix Renormalization Group
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• Bound on entanglement in neural quantum states
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Les Houches Lecture Notes on Tensor Networks
• Bardeen-Cooper-Schrieffer interaction as an infinite-range Penson-Kolb pairing mechanism
• The Complexity of Approximating Critical Points of Quantum Phase Transitions
• Constructing k-local parent Lindbladians for matrix product density operators
• Universality in Non-Equilibrium Quantum Systems
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Topologically ordered states in infinite quantum spin systems
• Role of external fields in enhancing long-distance entanglement at finite temperatures
• Gapped and gapless phases of frustration-free spin-1/2 chains
• Efficient classical simulation of cluster state quantum circuits with alternative inputs
• Volume-law entanglement entropy of typical pure quantum states
• Limitations on Dimensional Regularization in Renyi Entropy
• Clustering of steady-state correlations in open systems with long-range interactions
• Matrix Product State on a Quantum Computer
• Locally accurate tensor networks for thermal states and time evolution
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Non-Markovian steady states of a driven two-level system
• Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion
• Ranks of Tensor Networks for Eigenspace Projections and the Curse of Dimensionality
• Matrix-product entanglement characterizing the optimality of state-preparation quantum circuits
• Energy Spectra of Compressed Quantum States
• Quantum Machine Learning for State Tomography Using Classical Data
• Equivalence of Spatial and Particle Entanglement Growth After a Quantum Quench
• On the Ordering of Sites in the Density Matrix Renormalization Group using Quantum Mutual Information
• Fractal Path Strategies for Efficient 2D DMRG Simulations
• Quantum Circuits for Matrix-Product Unitaries
• Entanglement Complexity in Many-body Systems from Positivity Scaling Laws
• On ground state phases of quantum spin systems
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians
• Quantum Hall correlations in tilted extended Bose-Hubbard chains
• Dissipative dynamics in isolated quantum spin chains after a local quench
• Continuous matrix product operators for quantum fields
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• Insulating charge transfer ferromagnetism
• Global and short-range entanglement properties in excited, many-body localized spin chains
• Ground state energy and phase transitions of Long-range XXZ using VQE
• Universal Euler-Cartan Circuits for Quantum Field Theories
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Universal entanglement correction induced by relevant deformations at the quantum critical point
• Symmetry-enforced minimal entanglement and correlation in quantum spin chains
• Matrix product states and first quantization
• Entanglement entropy scaling laws from fluctuations of non-conserved quantities
• Tree tensor network impurity solver based on Cayley-tree mapping
• Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques
• The Canonical Forms of Matrix Product States in Infinite-Dimensional Hilbert Spaces
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States
• Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model
• Mutual information in interacting spin systems
• Entanglement signatures of a percolating quantum system
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Limits of Clifford Disentangling in Tensor Network States
• Efficient simulation of non-trivial dissipative spin chains via stochastic unraveling
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Knabe's spectral gap method for open boundary conditions
• Optimal bound on long-range distillable entanglement
• Coexistence of different scaling laws for the entanglement entropy in a periodically driven system
• Quantum entropy thermalization