Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain

Abstract

The density matrix renormalization group (``DMRG'') discovered by White has shown to be a powerful method to understand the properties of many one dimensional quantum systems. In the case where renormalization eventually converges to a fixed point we show that quantum states in the thermodynamic limit with periodic boundary conditions can be simply represented by a special type of product ground state with a natural description of Bloch states of elementary excitations that are spin-1 solitons. We then observe that these states can be rederived through a simple variational ansatz making no reference to a renormalization construction. The method is tested on the spin-1 Heisenberg model.

13 pages uuencoded compressed postscript including figures

References in corpus (2)

• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain

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• Self-Adaptive Tensor Network States with Multi-Site Correlators
• Matrix product state representation of quasielectron wave functions
• Matrix-Product based Projected Wave Functions Ansatz for Quantum Many-Body Ground States
• Matrix Product State Representation without explicit local Hilbert Space Truncation with Applications to the Sub-Ohmic Spin-Boson Model
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach
• PauliComposer: Compute Tensor Products of Pauli Matrices Efficiently
• Low-rank Riemannian eigensolver for high-dimensional Hamiltonians
• Converting long-range entanglement into mixture: tensor-network approach to local equilibration
• From SU(2)${}_5$ to SU(2)${}_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Certifying ground-state properties of quantum many-body systems
• A brief introduction to multipartite entanglement
• Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Entanglement renormalization and boundary critical phenomena
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group
• Single-Block Renormalization Group: Quantum Mechanical Problems
• Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions
• Construction of a matrix product stationary state from solutions of finite size system
• Fidelity and entanglement entropy for infinite-order phase transitions
• Characterizing the quantum field theory vacuum using temporal Matrix Product states
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Variational quantum state preparation via quantum data buses
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states
• Disentangling Sources of Quantum Entanglement in Quench Dynamics
• Holographic spin networks from tensor network states
• Tunable quantum criticality in multicomponent Rydberg arrays
• Triad second renormalization group
• Eight-vertex criticality in the interacting Kitaev chain
• Entanglement in Finitely Correlated Spin States
• Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms
• Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• Real-space renormalization group approach for the corner Hamiltonian
• Purity of thermal mixed quantum states
• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field
• Dimension of Tensor Network varieties
• Quantum error correction and large $N$
• Tensor network state correspondence and holography
• Multiple phase separation in one-dimensional mixtures of mass- and population-imbalanced attractive Fermi gases
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Computational complexity of non-equilibrium steady states of quantum spin chains
• Symmetries and entanglement in the one-dimensional spin-1/2 XXZ model
• Genuinely multi-point temporal quantum correlations and universal measurement-based quantum computing
• Tensor network methods with graph enhancement
• A Classical Background for the Wave Function Prediction in the Infinite System DMRG Method
• Scale-renormalized matrix-product states for correlated quantum systems
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• The seniority quantum number in Tensor Network States
• Majorana correlations in quantum impurities coupled to a topological wire
• How local is the information in MPS/PEPS tensor networks?
• Exact zero modes in frustrated Haldane chains
• tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train Format
• Reduced basis surrogates for quantum spin systems based on tensor networks
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Superconductivity in doped triangular Mott insulators: the roles of parent spin backgrounds and charge kinetic energy
• Extracting the Luttinger parameter from a single wave function
• Variational adiabatic transport of tensor networks
• Dynamical correlation functions from complex time evolution
• Partonic distribution functions and amplitudes using tensor network methods
• A simplified and improved approach to tensor network operators in two dimensions
• Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation on a frustrated ferromagnetic spin-$1/2$ chain
• Quantum Hamiltonian complexity and the detectability lemma
• Entanglement measures and the quantum to classical mapping
• U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
• Efficient tensor network algorithm for layered systems
• Numerical detection of symmetry enriched topological phases with space group symmetry
• 2D Multipartite Valence Bond States in Quantum Antiferromagnets
• Cumulants and Scaling Functions of Infinite Matrix Product States
• Two-Site shift Product Wave Function Renormalization Group Method Applied to Quantum Systems
• Connecting the von Neumann and Renyi entropies for Fermions
• Diagrammatics for SU(2) invariant matrix product states
• Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions
• Incommensurate structures studied by a modified Density Matrix Renormalization Group Method
• The dimer-RVB State of the Four-Leg Heisenberg Ladder: Interference among Resonances
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Recurrent Variational Approach to the Two-Leg Hubbard Ladder
• Density Matrix and Renormalization for Classical Lattice Models
• Critical properties of the quantum Ashkin-Teller chain with chiral perturbations
• Generalization of the tensor renormalization group approach to 3-D or higher dimensions
• Exact renormalization in quantum spin chains
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Tensor Renormalization Group Centered About a Core Tensor
• Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain
• Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme
• Rigorous decoupling between edge states in frustrated spin chains and ladders
• Phase Diagram of the Square-Lattice $t$-$J$-$V$ Model for Electron-Doped Cuprates
• Spatial Reflection and Associated String Order in Quantum Spin Chains
• The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
• Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals
• Matrix Product States with adaptive global symmetries
• Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems
• Uniform Matrix Product State in the Thermodynamic Limit
• Hilbert space renormalization for the many-electron problem
• Possible Observation of Quadrupole Waves in Spin Nematics
• Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems
• Hilbert space multireference coupled clusters tailored by matrix product states
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• On the Magnetization of the $120^{\circ }$ order of the Spin-1/2 Triangular Lattice Heisenberg Model: a DMRG revisit
• Size consistency of tensor network methods for quantum many-body systems
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Loop Series Expansions for Tensor Networks
• Inversion symmetry of singular values and a new orbital ordering method in tensor train approximations for quantum chemistry
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• Combination of Tensor Network States and Green's function Monte Carlo
• Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains
• Generalized mean field description of entanglement in dimerized spin systems
• Fast multidimensional convolution in low-rank formats via cross approximation
• Universal Characterization of Quantum Many-Body States through Local Information
• Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit
• Critical properties of the Majorana chain with competing interactions
• Infinite-size density matrix renormalization group with parallel Hida's algorithm
• 2D excitation information by MPS method on infinite helixes
• Tensor Network States with Three-Site Correlators
• From Lattice Gauge Theories to Hydrogen Atoms
• Quantum phases of spin-1 system on 3/4 and 3/5 skewed ladders
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• Ground-state properties of the one-dimensional Hubbard model with pairing potential
• Ground-state wavefunction of macroscopic electron systems
• Ground state of many-electron systems based on the action function
• Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
• Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Optimization of infinite projected entangled pair states: The role of multiplets and their breaking
• Non-classical correlations in a class of spin chains with long-range interactions and exactly solvable ground states
• Distinguishing Phases with Ansatz Wavefunctions
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Exact ground states for two new spin-1 quantum chains, new features of matrix product states
• Supersymmetry and multicriticality in a ladder of constrained fermions
• Quantum Dimensional Transition in Spin-$\frac{1}{2}$ Antiferromagnetic Heisenberg Model on A Square Lattice and Space Reduction in Matrix Product State
• Realization of Wess-Zumino-Witten transitions with levels $k=6$ and $k=4$ in a frustrated spin-3 chain
• An efficient perturbation theory of density matrix renormalization group
• Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line
• Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder
• Ground state and finite temperature behavior of 1/4-filled band zigzag ladders
• The Linear Span of Uniform Matrix Product States
• Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Direct interpolative construction of the discrete Fourier transform as a matrix product operator
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Thermodynamics of the Hubbard Model on the Bethe Lattice
• The Density Matrix Renormalization Group technique with periodic boundary conditions
• Effective One-Dimensional Models from Matrix Product States
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Matrix Product Approach to Conjugated Polymers
• Approximation, Proof Systems, and Correlations in a Quantum World
• Extended Delta-map: a map-based foreground removal method for CMB polarization observations
• Tensor Renormalization Group for interacting quantum fields
• Tensor network non-zero testing
• From Kosterlitz-Thouless to Pokrovsky-Talapov transitions in spinless fermions and spin chains with next-nearest neighbour interactions
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Spectroscopy with the tensor renormalization group method
• Matrix product states for $su(2)$ invariant quantum spin chains
• Quantum Corner-Transfer Matrix DMRG
• Wavefunction Vortex Attachment via Matrix Products: Application to Atomic Fermi Gases in Flat Spin-Orbit Bands
• Quantum Joule Expansion of One-Dimensional Systems
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Incommensurate Matrix Product State for Quantum Spin Systems
• Tangent Space Excitation Ansatz for Quantum Circuits
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Quantum generative modeling for financial time series with temporal correlations
• Block-Spin Approach to Electron Correlations
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Zero-site DMRG and the optimal low-rank correction
• Probing universal critical scaling with scan-DMRG
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Translation invariant tensor product states in a finite lattice system
• Improving accuracy of tree-tensor network approach by optimization of network structure
• Symmetry-Protected Local Minima in Infinite DMRG
• Quantum Magnetic Skyrmions on Kondo-type Lattices
• Fundamental role of nonlocal orders in 1D Extended Bose-Hubbard Model
• Decoherence and relaxation in the interacting quantum dot system
• Chiral Edge States Emerging on Anyon-Net
• Spatial reflection and renormalization group flow of quantum many-body systems with matrix product state representation
• Quantum simulation of spin-1/2 XYZ model using solid-state spin centers
• Inchworm tensor train hybridization expansion quantum impurity solver
• The Software Landscape for the Density Matrix Renormalization Group
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• Variational optimization of projected entangled-pair states on the triangular lattice
• Les Houches Lecture Notes on Tensor Networks
• Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
• Build your own tensor network library: DMRjulia I. Basic library for the density matrix renormalization group
• Valence bond ground states in quantum antiferromagnets and quadratic algebras
• Application of Uniform Matrix Product State to Quantum Phase Transition with a Periodicity Change
• Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks
• Implicitly disentangled renormalization
• Studies of braided non-Abelian anyons using anyonic tensor networks
• On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
• The infinite occupation number basis of bosons - solving a numerical challenge
• Entanglement distance between quantum states and its implications for density-matrix-renormalization-group study of degenerate ground-states
• Quantum Entanglement of Tensor Networks with Symmetry Projections
• Multilayer wave functions: A recursive coupling of local excitations
• Real-Space Renormalization Group Method Applied to Quantum Lattice Hamiltonians
• Parent Hamiltonian for Fully-augmented Matrix Product States
• Optimal Matrix Product States for the Heisenberg Spin Chain
• Accurate simulation and thermal tuning by temperature-adaptive boundary interactions on quantum many-body systems
• Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra
• Non-Markovian steady states of a driven two-level system
• Exponential Separation Criteria for Quantum Iterative Power Algorithms
• Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction
• Matrix Product State on a Quantum Computer
• Extrapolation-CAM Theory for Critical Exponents
• Low-rank representation of tensor network operators with long-range pairwise interactions
• DMRjulia: Tensor recipes for entanglement renormalization computations
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models
• Half-Chain Entanglement Entropy in the One-Dimensional Spinless Fermion Model
• Rényi entropy of the permutationally invariant part of the ground state across a quantum phase transition
• Global and short-range entanglement properties in excited, many-body localized spin chains
• Jacobi-Davidson method on low-rank matrix manifolds
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach
• Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
• Leaf-to-leaf distances in Catalan trees
• Solving the Holstein molecular crystal model
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?
• Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model
• Grassmann tensor networks
• Spurious Strange Correlators in Symmetry-Protected Topological Phases
• Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains"
• Single-hole spectral functions in one-dimensional quantum magnets with different ground states
• Solving intractable chemical problems by tensor decomposition
• Excitation and Entanglement Transfer Near Quantum Critical Points
• Entanglement-based tensor-network strong-disorder renormalization group
• A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain
• Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model
• Chasing infinity with matrix product states by embracing divergences
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• On the Ordering of Sites in the Density Matrix Renormalization Group using Quantum Mutual Information
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy