Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm

Abstract

An infinite projected entangled pair state (iPEPS) is a tensor network ansatz to represent a quantum state on an infinite 2D lattice whose accuracy is controlled by the bond dimension $D$. Its real, Lindbladian or imaginary time evolution can be split into small time steps. Every time step generates a new iPEPS with an enlarged bond dimension $D^{\prime }>D$, which is approximated by an iPEPS with the original $D$. In Phys. Rev. B 98, 045110 (2018) an algorithm was introduced to optimize the approximate iPEPS by maximizing directly its fidelity to the one with the enlarged bond dimension $D^{\prime }$. In this work we implement a more efficient optimization employing a local estimator of the fidelity. For imaginary time evolution of a thermal state's purification, we also consider using unitary disentangling gates acting on ancillas to reduce the required $D$. We test the algorithm simulating Lindbladian evolution and unitary evolution after a sudden quench of transverse field $h_x$ in the 2D quantum Ising model. Furthermore, we simulate thermal states of this model and estimate the critical temperature with good accuracy: $0.1\%$ for $h_x=2.5$ and $0.5\%$ for the more challenging case of $h_x=2.9$ close to the quantum critical point at $h_x=3.04438(2)$.

arXiv commentpublished version, presentation improved

References in corpus (65)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement renormalization
• An Area Law for One Dimensional Quantum Systems
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Area laws in quantum systems: mutual information and correlations
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Corner Transfer Matrix Renormalization Group Method
• Entropy scaling and simulability by Matrix Product States
• 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
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Fermionic Projected Entangled Pair States
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Gradient methods for variational optimization of projected entangled-pair states
• Dynamical phase diagram of spin chains with long-range interactions
• A positive tensor network approach for simulating open quantum many-body systems
• Magnetization of SrCu2(BO3)2 in ultrahigh magnetic fields up to 118 T
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Fermionic multi-scale entanglement renormalization ansatz
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• A simple tensor network algorithm for two-dimensional steady states
• Faster Methods for Contracting Infinite 2D Tensor Networks
• Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Excitations and the tangent space of projected entangled-pair states
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Unitary circuits for strongly correlated fermions
• Exponential Thermal Tensor Network Approach for Quantum Lattice Models
• Finite correlation length scaling with infinite projected entangled-pair states
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Signatures of the Many-body Localized Regime in Two Dimensions
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Optimized Decimation of Tensor Networks with Super-orthogonalization for Two-Dimensional Quantum Lattice Models
• Finding purifications with minimal entanglement
• Extending the range of real time density matrix renormalization group simulations
• Thermodynamics of Spin-1/2 Kagomé Heisenberg Antiferromagnet: Algebraic Paramagnetic Liquid and Finite-Temperature Phase Diagram
• Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
• Optimized contraction scheme for tensor-network states
• Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models
• Projected Entangled Pair States at Finite Temperature: Iterative Self-Consistent Bond Renormalization for Exact Imaginary Time Evolution
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Fermionic Projected Entangled Pair States at Finite Temperature
• A real space decoupling transformation for quantum many-body systems
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet

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• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• The Hubbard model: A computational perspective
• Quantum many-body dynamics in two dimensions with artificial neural networks
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• Lecture Notes of Tensor Network Contractions
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• A quantum magnetic analogue to the critical point of water
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
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• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase
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• Time Dependent Variational Principle for Tree Tensor Networks
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• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Tensor network study of the $m=1/2$ magnetization plateau in the Shastry-Sutherland model at finite temperature
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
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• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Systematic extraction of crystal electric-field effects and quantum magnetic model parameters in triangular rare-earth magnets
• Symmetric cluster expansions with tensor networks
• Two-body repulsive bound pairs in multi-body interacting Bose-Hubbard model
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice
• Entanglement and precession in two-dimensional dynamical quantum phase transitions
• Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition
• Variational classical networks for dynamics in interacting quantum matter
• Real-time operator evolution in two and three dimensions via sparse Pauli dynamics
• Variational quantum dynamics of two-dimensional rotor models
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
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• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point
• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
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• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Neural Projected Quantum Dynamics: a systematic study
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• Forecasting long-time dynamics in quantum many-body systems by dynamic mode decomposition
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• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Spectral functions with infinite projected entangled-pair states
• Thermal Tensor Network Simulations of the Heisenberg Model on the Bethe Lattice
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• Forestalled Phase Separation as the Precursor to Stripe Order
• Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
• Simulating chiral spin liquids with projected entangled-pair states
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Variational Neural and Tensor Network Approximations of Thermal States
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Quantum Gauge Networks: A New Kind of Tensor Network
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Truncating loopy tensor networks by zero-mode gauge fixing
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states