Simulating excitation spectra with projected entangled-pair states

Abstract

We develop and benchmark a technique for simulating excitation spectra of generic two-dimensional quantum lattice systems using the framework of projected entangled-pair states (PEPS). The technique relies on a variational ansatz for capturing quasiparticle excitations on top of a PEPS ground state. Our method perfectly captures the quasiparticle dispersion relation of the square-lattice transverse-field Ising model, and reproduces the spin-wave velocity and the spin-wave anomaly in the square-lattice Heisenberg model with high precision.

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Cited by in corpus (57)

• Tensor networks for complex quantum systems
• The Hubbard model: A computational perspective
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Collisions of false-vacuum bubble walls in a quantum spin chain
• Excitations with projected entangled pair states using the corner transfer matrix method
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets
• Gaussian time dependent variational principle for the Bose-Hubbard model
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Accurate simulation for finite projected entangled pair states in two dimensions
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Simulating 2+1d ${\mathbb{Z}}_3$ lattice gauge theory with iPEPS
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Direct sampling of projected entangled-pair states
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Variational methods for contracting projected entangled-pair states
• Entanglement order parameters and critical behavior for topological phase transitions and beyond
• A beginner's guide to non-abelian iPEPS for correlated fermions
• Real-time scattering of interacting quasiparticles in quantum spin chains
• Optimal sampling of dynamical large deviations via matrix product states
• Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics
• Symmetric cluster expansions with tensor networks
• Spinon confinement and deconfinement in spin-1 chains
• Generating Function for Tensor Network Diagrammatic Summation
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• TeNeS: Tensor Network Solver for Quantum Lattice Systems
• Generating function for projected entangled-pair states
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Extracting the Speed of Light from Matrix Product States
• Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories
• Efficient tensor network algorithm for layered systems
• Spectral functions with infinite projected entangled-pair states
• Momentum-resolved time evolution with matrix product states
• Fermionic Isometric Tensor Network States in Two Dimensions
• Possible Observation of Quadrupole Waves in Spin Nematics
• Detecting emergent continuous symmetries at quantum criticality
• 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
• Low-temperature Gibbs states with tensor networks
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Phase diagram of the Hubbard model on a square lattice: A cluster slave-spin study
• Simulating chiral spin liquids with projected entangled-pair states
• Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Adiabatic ground state preparation in an expanding lattice
• Accelerating two-dimensional tensor network optimization by preconditioning
• Tangent Space Excitation Ansatz for Quantum Circuits
• A Generalised Haldane Map from the Matrix Product State Path Integral to the Critical Theory of the $J_1$-$J_2$ Chain
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems