Generating function for projected entangled-pair states

Abstract

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating function approach for tensor network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-$1/2$ transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-$1/2$ $J_1$-$J_2$ model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multi-particle excitations.

arXiv comment13 pages, 6 figures

References in corpus (83)

• Area laws for the entanglement entropy - a review
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Tensor renormalization group approach to 2D classical lattice models
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Corner Transfer Matrix Renormalization Group Method
• Coarse-graining renormalization by higher-order singular value decomposition
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• PEPS as ground states: degeneracy and topology
• Second Renormalization of Tensor-Network States
• Fractional excitations in the square-lattice quantum antiferromagnet
• Differentiable Programming Tensor Networks
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Post-Matrix Product State Methods: To tangent space and beyond
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• Tangent-space methods for uniform matrix product states
• Tensor network study of the Shastry-Sutherland model in zero magnetic field
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Matrix product states for gauge field theories
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Resonating valence bond states in the PEPS formalism
• Variational matrix product ansatz for dispersion relations
• Tensor Network Algorithms: a Route Map
• A simple tensor network algorithm for two-dimensional steady states
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Faster Methods for Contracting Infinite 2D Tensor Networks
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• A quantum magnetic analogue to the critical point of water
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Excitations and the tangent space of projected entangled-pair states
• Elementary excitations in gapped quantum spin systems
• Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
• Finite correlation length scaling with infinite projected entangled-pair states
• A tensor network annealing algorithm for two-dimensional thermal states
• Period 4 stripe in the extended two-dimensional Hubbard model
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice
• Quantum critical phase with infinite projected entangled paired states
• The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• Simulating excitation spectra with projected entangled-pair states
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors
• Collisions of false-vacuum bubble walls in a quantum spin chain
• Excitations with projected entangled pair states using the corner transfer matrix method
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Mutually attracting spin waves in the square-lattice quantum antiferromagnet
• Quasiparticles in quantum spin chains with long-range interactions
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets
• Quantum Dynamics of the Square-Lattice Heisenberg Model
• Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Hole Spectral Function of a Chiral Spin Liquid in the Triangular Lattice Hubbard Model
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Variational methods for contracting projected entangled-pair states
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• A scaling hypothesis for projected entangled-pair states
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Spinon confinement and deconfinement in spin-1 chains
• Generating Function for Tensor Network Diagrammatic Summation
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Tensor Networks Can Resolve Fermi Surfaces
• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
• Automatic Differentiable Numerical Renormalization Group
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Determining non-Abelian topological order from infinite projected entangled pair states
• Field-induced Bose-Einstein condensation and supersolid in the two-dimensional Kondo necklace
• Variational Tensor Network Operator
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary

Cited by in corpus (12)

• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Spectral functions with infinite projected entangled-pair states
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Tangent Space Excitation Ansatz for Quantum Circuits
• Variational optimization of projected entangled-pair states on the triangular lattice
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS