Parallel time-dependent variational principle algorithm for matrix product states
arXiv:1912.06127 · doi:10.1103/PhysRevB.101.235123
Abstract
Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum lattice systems with long-range interactions. We benchmark the accuracy and performance of the algorithm by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes, with parallel efficiencies as high as 86%. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX spin chain with interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.
arXiv commentVersion accepted for publication in Phys. Rev. B. Text clarified and references updated. Main text: 11 pages, 13 figures. Appendices: 3 pages, 3 figures. Supplemental material: 4 pages, 3 figures
References in corpus (110)
- The density-matrix renormalization group in the age of matrix product states
- Area laws for the entanglement entropy - a review
- Efficient classical simulation of slightly entangled quantum computations
- Many-body localization, thermalization, and entanglement
- Efficient simulation of one-dimensional quantum many-body systems
- Time-dependence of correlation functions following a quantum quench
- Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- A toolbox for lattice spin models with polar molecules
- Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
- Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
- Many-body localization in a quantum simulator with programmable random disorder
- Realizing a lattice spin model with polar molecules
- Effective quantum spin systems with ion traps
- Observation of entanglement propagation in a quantum many-body system
- Time-dependent variational principle for quantum lattices
- A Rydberg Quantum Simulator
- Unifying time evolution and optimization with matrix product states
- Non-local propagation of correlations in long-range interacting quantum systems
- Matrix product states represent ground states faithfully
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Time-evolution methods for matrix-product states
- Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
- From density-matrix renormalization group to matrix product states
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
- Entropy scaling and simulability by Matrix Product States
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Studying Two Dimensional Systems With the Density Matrix Renormalization Group
- Matrix product operator representations
- Many-body interferometry of a Rydberg-dressed spin lattice
- Real time confinement following a quantum quench to a non-integrable model
- Spread of correlations in long-range interacting quantum systems
- Time-evolving a matrix product state with long-ranged interactions
- Minimally Entangled Typical Thermal State Algorithms
- The Ergodic Side of the Many-Body Localization Transition
- 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
- Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
- Entanglement entropy for the long range Ising chain
- Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems
- Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems
- Finding Exponential Product Formulas of Higher Orders
- Density matrix renormalization group algorithms with a single center site
- Entanglement growth in quench dynamics with variable range interactions
- Algorithms for finite Projected Entangled Pair States
- Scrambling and entanglement spreading in long-range spin chains
- Dynamical phase diagram of spin chains with long-range interactions
- Time-step targetting methods for real-time dynamics using DMRG
- Applying matrix product operators to model systems with long-range interactions
- Time integration of tensor trains
- A Strictly Single-Site DMRG Algorithm with Subspace Expansion
- Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
- Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
- Breakdown of quasilocality in long-range quantum lattice models
- Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains
- Time evolution algorithms for Matrix Product States and DMRG
- Finite automata for caching in matrix product algorithms
- Isometric Tensor Network States in Two Dimensions
- Unifying Projected Entangled Pair States contractions
- Persistence of locality in systems with power-law interactions
- Finite speed of quantum scrambling with long range interactions
- Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution
- Large-scale quantum-dynamics with matrix product states
- Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
- Functional renormalization for spontaneous symmetry breaking in the Hubbard model
- Strictly linear light cones in long-range interacting systems of arbitrary dimensions
- Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
- Out of equilibrium dynamics with Matrix Product States
- Time dynamics with matrix product states: Many-body localization transition of large systems revisited
- Infinite boundary conditions for matrix product state calculations
- Real-Space Parallel Density Matrix Renormalization Group
- Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
- Time-dependent Density Matrix Renormalization Group Quantum Dynamics for Realistic Chemical Systems
- Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
- Tensor operators: constructions and applications for long-range interaction systems
- Quasi-localized excitations induced by long-range interactions in translationally-invariant quantum spin chains
- Geometry of Matrix Product States: metric, parallel transport and curvature
- Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
- Numerical Assessment for Accuracy and GPU Acceleration of TD-DMRG Time Evolution Schemes
- Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions
- Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
- Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
- Density matrix renormalization group on a cylinder in mixed real and momentum space
- Origin of the slow growth of entanglement entropy in long-range interacting spin systems
- Breaking the entanglement barrier: Tensor network simulation of quantum transport
- Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium
- Multi-set matrix product state calculations reveal mobile Franck-Condon excitations under strong Holstein-type coupling
- Time Dependent Variational Principle for Tree Tensor Networks
- Error estimates for extrapolations with matrix-product states
- Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension
- Quantum dynamics of disordered spin chains with power-law interactions
- The operator Lévy flight: light cones in chaotic long-range interacting systems
- Emergent locality in systems with power-law interactions
- Multigrid Renormalization
- Effect of long-range hopping and interactions on entanglement dynamics and many-body localization
- Performance of the time-dependent variational principle for matrix product states in long-time evolution of a pure state
- The Tensor Network Theory Library
- Parallelization Strategies for Density Matrix Renormalization Group Algorithms on Shared-Memory Systems
- Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions
- Dynamical Phase Diagram of a Quantum Ising Chain with Long Range Interactions
- Matrix product state formulation of the multiconfiguration time-dependent Hartree theory
- Spin transport in long-range interacting one-dimensional chain
- The density matrix renormalization group algorithm on kilo-processor architectures: implementation and trade-offs
- Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems
- Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG
- Towards overcoming the entanglement barrier when simulating long-time evolution
- Disentangling Sources of Quantum Entanglement in Quench Dynamics
- Propagating large open quantum systems towards their steady states: cluster implementation of the time-evolving block decimation scheme
- Infinite-size density matrix renormalization group with parallel Hida's algorithm
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- Beyond-classical computation in quantum simulation
- Low communication high performance ab initio density matrix renormalization group algorithms
- Hierarchy of linear light cones with long-range interactions
- Tree tensor network state approach for solving hierarchical equations of motion
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- Density Matrix Renormalization Group with Tensor Processing Units
- Collective neutrino oscillations with tensor networks using a time-dependent variational principle
- Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer
- Time-dependent variational principle with controlled bond expansion for matrix product states
- Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons
- Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
- Optimal Tree Tensor Network Operators for Tensor Network Simulations: Applications to Open Quantum Systems
- Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
- Floquet-induced localization in long-range many-body systems
- Quantized tensor networks for solving the Vlasov-Maxwell equations
- Fast Time-Evolution of Matrix-Product States using the QR decomposition
- Tensor product approach to modelling epidemics on networks
- Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D
- Suppressing Decoherence in Quantum Plasmonic Systems by Spectral Hole Burning Effect
- Non-equilibrium boundary driven quantum systems: models, methods and properties
- Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
- Many-body computing on Field Programmable Gate Arrays
- Simulating quantum dynamics: Evolution of algorithms in the HPC context
- Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
- Approximate Quadratization of High-Order Hamiltonians for Combinatorial Quantum Optimization
- Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors