Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model

Abstract

We generalize the Matrix Product States method using the chiral vertex operators of Conformal Field Theory and apply it to study the ground states of the XXZ spin chain, the J1-J2 model and random Heisenberg models. We compute the overlap with the exact wave functions, spin-spin correlators and the Renyi entropy, showing that critical systems can be described by this method. For rotational invariant ansatzs we construct an inhomogenous extension of the Haldane-Shastry model with long range exchange interactions.

5 pages, 4 figures, 1 reference added

References in corpus (4)

• Matrix product states represent ground states faithfully
• Renormalization and tensor product states in spin chains and lattices
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Criticality and entanglement in random quantum systems

Cited by in corpus (103)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Time-evolving a matrix product state with long-ranged interactions
• Continuous Matrix Product States for Quantum Fields
• The mass spectrum of the Schwinger model with Matrix Product States
• Entanglement entropy of two disjoint blocks in XY chains
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Topology and edge modes in quantum critical chains
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Unusual Corrections to Scaling in Entanglement Entropy
• Entanglement entropy of critical spin liquids
• Exact Matrix Product States for Quantum Hall Wave Functions
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Calculus of continuous matrix product states
• Entanglement spectrum of random-singlet quantum critical points
• The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation
• Matrix Product States for Trial Quantum Hall States
• Quantum spin Hamiltonians for the SU(2)_k WZW model
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Full counting statistics in the Haldane-Shastry chain
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Nonadditive entropy for random quantum spin-S chains
• Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field
• Continuous Tensor Network States for Quantum Fields
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Infinite Matrix Product States for long range SU(N) spin models
• Truncated Conformal Space Approach for Perturbed Wess-Zumino-Witten $SU(2{)}_k$ Models
• Quantum many-body scars with chiral topological order in 2D and critical properties in 1D
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• Chiral correlators of the Ising conformal field theory
• Computable Rényi mutual information: Area laws and correlations
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
• Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Violation of the area law and long range correlations in infinite matrix product states
• Yangian-invariant spin models and Fibonacci numbers
• Matrix product state representation of quasielectron wave functions
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Many-body delocalization via symmetry emergence
• Bosonic fractional quantum Hall states on the torus from conformal field theory
• Integrable open spin chains related to infinite matrix product states
• Excited States in Spin Chains from Conformal Blocks
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• Compact Neural-network Quantum State representations of Jastrow and Stabilizer states
• Lattice Laughlin states on the torus from conformal field theory
• Model wavefunctions for interfaces between lattice Laughlin states
• Extracting the Luttinger parameter from a single wave function
• Escaping many-body localization in an exact eigenstate
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Gutzwiller Approach for Elementary Excitations in $S=1$ Antiferromagnetic Chains
• Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations
• Exact renormalization in quantum spin chains
• Laughlin topology on fractal lattices without area law entanglement
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Multipartite entanglement in spin chains and the Hyperdeterminant
• Bosonic Gaussian states from conformal field theory
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Field Tensor Network States
• Construction of spin models displaying quantum criticality from quantum field theory
• Many-body Lattice Wavefunctions From Conformal Blocks
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Exactly solvable quantum impurity model with inverse-square interactions
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Disordered Haldane-Shastry model
• A novel class of translationally invariant spin chains with long-range interactions
• Quantum Tensor Networks, Stochastic Processes, and Weighted Automata
• Properties of Laughlin states on fractal lattices
• The open Haldane-Shastry chain: thermodynamics and criticality
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• Crystalline invariants of fractional Chern insulators
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Effective description of correlations for states obtained from conformal field theory
• Generalised ansatz for continuous Matrix Product States
• Exact bosonic Matrix Product States (and holography)
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Chain and ladder models with two-body interactions and analytical ground states
• Symmetries and field tensor network states
• Quantum impurity models from conformal field theory
• Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid
• Local Hamiltonians for one-dimensional critical models