Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)

Abstract

We have studied the system of hard-core bosons on a 2-D optical lattice using a variational algorithm based on projected entangled-pair states (PEPS). We have investigated the ground state properties of the system as well as the responses of the system to sudden changes in the parameters. We have compared our results to mean field results based on a Gutzwiller ansatz.

9 pages, 9 figures

References in corpus (3)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)

Cited by in corpus (206)

• Area laws for the entanglement entropy - a review
• 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
• Unifying time evolution and optimization with matrix product states
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Fidelity approach to quantum phase transitions
• Tensor networks for complex quantum systems
• The iTEBD algorithm beyond unitary evolution
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Renormalization and tensor product states in spin chains and lattices
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Scaling of entanglement support for Matrix Product States
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Tensor network states and geometry
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Fermionic Projected Entangled Pair States
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Quantum information analysis of electronic states at different molecular structures
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• Matrix Product States for dynamical simulation of infinite chains
• A positive tensor network approach for simulating open quantum many-body systems
• Renormalization of tensor-network states
• Ground state fidelity from tensor network representations
• Variational quantum Monte Carlo simulations with tensor-network states
• Fermionic multi-scale entanglement renormalization ansatz
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• Variational matrix product ansatz for dispersion relations
• Finite automata for caching in matrix product algorithms
• Perfect Sampling with Unitary Tensor Networks
• Tensor Network Algorithms: a Route Map
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Unifying Projected Entangled Pair States contractions
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• An information theoretical analysis of quantum optimal control
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Excitations and the tangent space of projected entangled-pair states
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Quantum MERA Channels
• Monte Carlo simulation with Tensor Network States
• Infinite boundary conditions for matrix product state calculations
• A hierarchy of topological tensor network states
• Real-time simulation of the Schwinger effect with Matrix Product States
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Hamiltonian simulation of the Schwinger model at finite temperature
• Tensor operators: constructions and applications for long-range interaction systems
• Geometry of Matrix Product States: metric, parallel transport and curvature
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• General-purpose quantum circuit simulator with Projected Entangled-Pair States and the quantum supremacy frontier
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Faster identification of optimal contraction sequences for tensor networks
• Tensor networks and the numerical renormalization group
• A class of highly entangled many-body states that can be efficiently simulated
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice
• The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Time Dependent Variational Principle for Tree Tensor Networks
• Quantum Phases of Trapped Ions in an Optical Lattice
• Simulation of time evolution with the MERA
• Excitations with projected entangled pair states using the corner transfer matrix method
• Realizing the two-dimensional hard-core Bose-Hubbard model with superconducting qubits
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Time-dependent study of disordered models with infinite projected entangled pair states
• Sequentially generated states for the study of two dimensional systems
• Tensor product representation of topological ordered phase: necessary symmetry conditions
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics
• Efficient simulation of Grassmann Tensor Product States
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Multigrid Renormalization
• Fourier transform of fermionic systems and the spectral tensor network
• Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States
• Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz
• The Algebraic Bethe Ansatz and Tensor Networks
• Enhanced noise resilience of the surface-GKP code via designed bias
• Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice
• 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
• Tensor network states in time-bin quantum optics
• Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
• Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Absence of static stripes in the two-dimensional $t-J$ model by an accurate and systematic quantum Monte Carlo approach
• Finite-Size Geometric Entanglement from Tensor Network Algorithms
• Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices
• Projected Entangled Pair States at Finite Temperature: Iterative Self-Consistent Bond Renormalization for Exact Imaginary Time Evolution
• Quantum quenches in two spatial dimensions using chain array matrix product states
• Entanglement patterns and generalized correlation functions in quantum many body systems
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Multiconfiguration time-dependent Hartree impurity solver for nonequilibrium dynamical mean-field theory
• Non-local correlations in the Haldane phase for an XXZ spin-1 chain: A perspective from infinite matrix product state representation
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Stability of mixed-state quantum phases via finite Markov length
• Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states
• Gauging tensor networks with belief propagation
• Fermionic Projected Entangled Pair States at Finite Temperature
• Symmetry breaking and criticality in tensor-product states
• Concatenated tensor network states
• Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments
• Continuum tensor network field states, path integral representations and the encoding of spatial symmetries
• The area law and real-space renormalization
• Further developments in correlator product states: deterministic optimization and energy evaluation
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Critical exponents of one-dimensional quantum critical models by means of MERA tensor network
• Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition
• Comb tensor networks
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
• Tensor network simulation of the Kitaev-Heisenberg model at finite temperature
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States
• General tensor network decoding of 2D Pauli codes
• Renormalization algorithm with graph enhancement
• Ultracold atomic Bose and Fermi spinor gases in optical lattices
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Quantum fidelity for degenerate groundstates in quantum phase transitions
• A variational method based on weighted graph states
• Homogeneous MERA states: an information theoretical analysis
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Finite temperature properties of strongly correlated systems via variational Monte Carlo
• Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
• Systematic construction of density functionals based on matrix product state computations
• Variational classical networks for dynamics in interacting quantum matter
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• Spin ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet
• Variational Monte Carlo simulations using tensor-product projected states
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Tensor Network Decoding Beyond 2D
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• Local Hamiltonians in Quantum Computation
• Efficient representation of long-range interactions in tensor network algorithms
• Finite Projected Entangled Pair States for the Hubbard model
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
• Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
• The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Persistence of entanglement in thermal states of spin systems
• Entanglement renormalization and boundary critical phenomena
• Configuration Interaction with Antisymmetrized Geminal Powers
• Determining non-Abelian topological order from infinite projected entangled pair states
• Tensor network methods with graph enhancement
• Exact dimer ground states for a continuous family of quantum spin chains
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States
• Efficient tensor network algorithm for layered systems
• Determining topological order from infinite projected entangled pair states
• Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Short-time vs. long-time dynamics of entanglement in quantum lattice models
• Simulation of gauge transformations on systems of ultracold atoms
• Mixed-state phase transitions in spin-Holstein models
• Lattice bosons in quartic confinement
• Competing States in the Two-Dimensional Frustrated Kondo-Necklace Model
• Size consistency of tensor network methods for quantum many-body systems
• Quantum phases of spin-1 system on 3/4 and 3/5 skewed ladders
• Optimization of infinite projected entangled pair states: The role of multiplets and their breaking
• Entanglement Continuous Unitary Transformations
• Fermionic tensor network contraction for arbitrary geometries
• Tensor networks and efficient descriptions of classical data
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Matrix product states for $su(2)$ invariant quantum spin chains
• Simulation of Quantum Many-Body Systems on Amazon Cloud
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Positive bias makes tensor-network contraction tractable
• Efficient certification and simulation of local quantum many-body Hamiltonians
• An exact real-space renormalization method and applications
• Simulating quantum dynamics: Evolution of algorithms in the HPC context
• Variational methods for characterizing matrix product operator symmetries
• The infinite occupation number basis of bosons - solving a numerical challenge
• Computing quantum phase transitions
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Shot-noise reduction for lattice Hamiltonians
• Multilayer wave functions: A recursive coupling of local excitations
• Efficient 2D Tensor Network Simulation of Quantum Systems
• Tensor network states for the description of quantum many-body systems
• Truncating loopy tensor networks by zero-mode gauge fixing