Entanglement spectrum and boundary theories with projected entangled-pair states

Abstract

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models, like a deformed AKLT [1], an Ising-type [2], and Kitaev's toric code [3], both in finite ladders and infinite square lattices. In the latter case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.

13 pages, 14 figures

References in corpus (12)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Matrix product states represent ground states faithfully
• Area laws in quantum systems: mutual information and correlations
• Criticality, the area law, and the computational power of PEPS
• Valence Bond Solids for Quantum Computation
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Continuous Matrix Product States for Quantum Fields
• Entropy and Entanglement in Quantum Ground States
• Holographic quantum states
• Entanglement in valence-bond-solid states on symmetric graphs

Cited by in corpus (233)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Learning phase transitions by confusion
• Quantum entanglement in condensed matter systems
• Tensor networks for complex quantum systems
• Quantum Entanglement in Neural Network States
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• Lecture Notes of Tensor Network Contractions
• Loop optimization for tensor network renormalization
• Resonating valence bond states in the PEPS formalism
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Unifying Projected Entangled Pair States contractions
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Exact Matrix Product States for Quantum Hall Wave Functions
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• How universal is the entanglement spectrum?
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Renyi Entropies for Free Field Theories
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Quantum critical phase with infinite projected entangled paired states
• Shadows of Anyons
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Entanglement spectroscopy on a quantum computer
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Entanglement Hamiltonian of Interacting Fermionic Models
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Chiral topological spin liquids with projected entangled pair states
• Efficient representation of fully many-body localized systems using tensor networks
• Residual entropies for three-dimensional frustrated spin systems with tensor networks
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Chiral projected entangled-pair state with topological order
• Entanglement phases as holographic duals of anyon condensates
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• On the relation between entanglement and subsystem Hamiltonians
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
• The entanglement spectrum of chiral fermions on the torus
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Edge theories in Projected Entangled Pair State models
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Tensor network wavefunction of $S=1$ Kitaev spin liquids
• Bridging Perturbative Expansions with Tensor Networks
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• On the continuum limit of the entanglement Hamiltonian
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Entanglement polarization for the topological quadrupole phase
• Entanglement Thermodynamics
• Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States
• Detection of Symmetry Enriched Topological Phases
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Continuous Tensor Network States for Quantum Fields
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Entanglement Spectroscopy using Quantum Monte Carlo
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
• Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
• Construction of Hamiltonians by supervised learning of energy and entanglement spectra
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Universal entropy of conformal critical theories on a Klein bottle
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Z2 topological liquid of hard-core bosons on a kagome lattice at 1/3 filling
• Entanglement order parameters and critical behavior for topological phase transitions and beyond
• Featureless quantum insulator on the honeycomb lattice
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Critical entanglement spectrum of one-dimensional symmetry protected topological phases
• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Excitation spectrum of spin-1 Kitaev spin liquids
• Identifying Symmetry-Protected Topological Order by Entanglement Entropy
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Trimer states with ${\mathbb{Z}}_3$ topological order in Rydberg atom arrays
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Tree tensor networks and entanglement spectra
• A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians
• Entanglement Chern number for an extensive partition of a topological ground state
• Theory of competing Chern-Simons orders and emergent phase transitions
• The entanglement and relative entropy of a chiral fermion on the torus
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Bond Order via Light-Induced Synthetic Many-body Interactions of Ultracold Atoms in Optical Lattices
• Topological and dynamical properties of a generalized cluster model in one dimension
• Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
• Emergent conformal boundaries from finite-entanglement scaling in matrix product states
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• Detecting Topological Order with Ribbon Operators
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states
• Bosonic symmetry protected topological phases with reflection symmetry
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• The Heisenberg XX spin chain and low-energy QCD
• Global anomaly detection in two-dimensional symmetry-protected topological phases
• Long range order and symmetry breaking in Projected Entangled Pair State models
• Semionic resonating valence bond states
• Product vacua with boundary states and the classification of gapped phases
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Boson condensation and instability in the tensor network representation of string-net states
• Mathematical open problems in Projected Entangled Pair States
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Quantum phase transition between symmetry enriched topological phases in tensor-network states
• Local convertibility of the ground state of the perturbed Toric code
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Locality at the boundary implies gap in the bulk for 2D PEPS
• On tensor network representations of the (3+1)d toric code
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy
• The minimal canonical form of a tensor network
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Field-induced superfluids and Bose liquids in Projected Entangled Pair States
• Characterizing MPS and PEPS Preparable via Measurement and Feedback
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Determining non-Abelian topological order from infinite projected entangled pair states
• Entanglement Hamiltonian of the quantum Néel state
• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Locally purified density operators for noisy quantum circuits
• Determining topological order from infinite projected entangled pair states
• Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Determining the structure of real-space entanglement spectrum from approximate conditional independence
• Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases
• Numerical detection of symmetry enriched topological phases with space group symmetry
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
• Tunneling-induced restoration of classical degeneracy in quantum kagome ice
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Locality of Edge States and Entanglement Spectrum from Strong Subadditivity
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• SU(4) topological RVB spin liquid on the square lattice
• Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• Quantum Compression of Tensor Network States
• Holographic encoding of universality in corner spectra
• Classification of trivial spin-1 tensor network states on a square lattice
• Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Locality estimes for complex time evolution in 1D
• Entanglement gap, corners, and symmetry breaking
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Variational Tensor Network Operator
• Simulating chiral spin liquids with projected entangled-pair states
• Topological quantum phase transitions in a Majorana chain with spatial modulation
• Classifying parafermionic gapped phases using matrix product states
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Preparing matrix product states via fusion: constraints and extensions
• Entanglement studies of interacting fermionic models
• On integrable matrix product operators with bond dimension $D=4$
• Time Evolution and Deterministic Optimisation of Correlator Product States
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Entanglement spectrum of the degenerative ground state of Heisenberg ladders in a time-dependent magnetic field
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• Simulation of the Ring-exchange Models with Projected Entangled Pair States
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Entanglement in the Quantum Spherical Model -- a Review
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• A Simple and General Equation for Matrix Product Unitary Generation
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Deformations of the Boundary Theory of the Square Lattice AKLT Model
• Entanglement gap in 1D long-range quantum spherical models
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States
• ${\mathbb{Z}}_N$ symmetry breaking in Projected Entangled Pair State models
• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• A useful way to obtain the central charge of entanglement Hamiltonian -- Nested entanglement entropy
• Parent Lindbladians for Matrix Product Density Operators
• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Dynamical Geometry of the Haldane Model under a Quantum Quench
• Tensor network states for the description of quantum many-body systems
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Entanglement Trajectory and its Boundary
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires