Classical simulation of infinite-size quantum lattice systems in two spatial dimensions

Abstract

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac, cond-mat/0407066] and the infinite {\em time-evolving block decimation} algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analysing its second order quantum phase transition.

4 pages, 6 figures, 1 table. Revised version, with new diagrams and plots. The results on classical systems can now be found at arXiv:0711.3960

References in corpus (8)

• Efficient classical simulation of slightly entangled quantum computations
• Efficient simulation of one-dimensional quantum many-body systems
• Entanglement renormalization
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• A class of quantum many-body states that can be efficiently simulated
• The iTEBD algorithm beyond unitary evolution
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Entanglement renormalization and topological order

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• Tensor network study of the Shastry-Sutherland model with weak interlayer coupling
• Loop Series Expansions for Tensor Networks
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• Competing States in the Two-Dimensional Frustrated Kondo-Necklace Model
• Tensor-network approach to thermalization in open quantum many-body systems
• Combination of Tensor Network States and Green's function Monte Carlo
• Locality optimization for parent Hamiltonians of Tensor Networks
• Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder
• Field induced non-BEC transitions in frustrated magnets
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries
• Variational Tensor Network Operator
• Quantum computing quantum Monte Carlo algorithm
• Ground-state properties via machine learning quantum constraints
• Floating Phases in One-Dimensional Rydberg Ising Chains
• Single-layer tensor network approach for three-dimensional quantum systems
• Forestalled Phase Separation as the Precursor to Stripe Order
• Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
• Optimization of infinite projected entangled pair states: The role of multiplets and their breaking
• 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
• On Stability of Tensor Networks and Canonical Forms
• The resource theory of tensor networks
• Entanglement Continuous Unitary Transformations
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Detecting Confined and Deconfined Spinons in Dynamical Quantum Simulations
• Simulating chiral spin liquids with projected entangled-pair states
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Efficient conversion from fermionic Gaussian states to matrix product states
• Exploiting the Hermitian symmetry in tensor network algorithms
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics
• Imaginary-time relaxation quantum critical dynamics in two-dimensional dimerized Heisenberg model
• Frustration-Induced Supersolid Phases of Extended Bose-Hubbard Model in the Hard-Core Limit
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• Simulation of Quantum Many-Body Systems on Amazon Cloud
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Density Matrix Embedding Theory and Strongly Correlated Lattice Systems
• Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Loop update for infinite projected entangled-pair states in two spatial dimensions
• Plaquette valence bond state in spin-1/2 J1-J2 XY model on square lattice
• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Scalable projected entangled-pair state representation of random quantum circuit states
• Adiabatic ground state preparation in an expanding lattice
• Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice
• Simulating quantum dynamics: Evolution of algorithms in the HPC context
• Incommensurate Matrix Product State for Quantum Spin Systems
• Markov-chain sampling for long-range systems without evaluating the energy
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite basis limit
• Multilayer wave functions: A recursive coupling of local excitations
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Lifshitz transition in the phase diagram of two-leg $t$-$J$ ladder systems at low filling
• Implicitly disentangled renormalization
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Phonon-induced disorder in dynamics of optically pumped metals from non-linear electron-phonon coupling
• Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States
• Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations
• Optimal sampling of tensor networks targeting wave function's fast decaying tails
• The Hubbard model with fermionic tensor networks
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Variational boundary based tensor network renormalization group
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Magnetic phases of the periodic Anderson model in two dimensions
• Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
• Efficient 2D Tensor Network Simulation of Quantum Systems
• Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
• Dissipative dynamics in isolated quantum spin chains after a local quench
• Nonequilibrium dark space phase transition
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
• Truncating loopy tensor networks by zero-mode gauge fixing
• Non-Hermitian Lindhard function and Friedel oscillations
• Imaginary Time Spectral Transforms for Excited State Preparation
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators
• Chasing infinity with matrix product states by embracing divergences
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach
• Grassmann tensor networks
• Limits of Clifford Disentangling in Tensor Network States
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice
• Itinerant magnetism in the triangular lattice Hubbard model at half-doping: Application to twisted transition-metal dichalcogenides
• Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS
• Topology-driven phase transitions in the classical monomer-dimer-loop model
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states
• Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?
• Low-rank representation of tensor network operators with long-range pairwise interactions
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Embracing divergence: a formalism for when your semiring is simply not complete, with applications in quantum simulation