Light Cone Matrix Product

Abstract

We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at $\Delta =0.5$, we simulate to a time of $\approx 22.5$. While part of the long simulation time is due to the use of the light-cone method, we also describe a modification of the iTEBD algorithm with improved numerical stability, and we describe how to incorporate symmetry into this algorithm. While statistical sampling error means that we are not yet able to make a definite statement, the behavior of the simulation at long times indicates the appearance of either "revivals" in the order parameter as predicted previously or of a distinct shoulder in the decay of the order parameter.

15 pages, 6 figures

References in corpus (7)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• General entanglement scaling laws from time evolution
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

Cited by in corpus (36)

• The density-matrix renormalization group in the age of matrix product states
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Variational optimization algorithms for uniform matrix product states
• Hamiltonian complexity
• Hardware-efficient variational quantum algorithms for time evolution
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Propagation front of correlations in an interacting Bose gas
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Locality and digital quantum simulation of power-law interactions
• Connecting Entanglement in Time and Space: Improving the Folding Algorithm
• Extending the range of real time density matrix renormalization group simulations
• Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
• Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
• Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit
• Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
• Scaling of temporal entanglement in proximity to integrability
• Quantum quenches in two spatial dimensions using chain array matrix product states
• Light-cone velocities after a global quench in a non-interacting model
• Light cone tensor network and time evolution
• Local variational quantum compilation of a large-scale Hamiltonian dynamics
• Simulating the Dynamics of Single Photons in BosonSampling Devices with Matrix Product States
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Fast Time-Evolution of Matrix-Product States using the QR decomposition
• Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects
• Exactly solvable many-body dynamics from space-time duality
• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Asymptotically Decreasing Lieb-Robinson Velocity for a Class of Dissipative Quantum Dynamics
• Energy-band echoes: Time-reversed light emission from optically driven quasiparticle wavepackets
• Ground state of many-electron systems based on the action function
• Ground-state wavefunction of macroscopic electron systems
• Differentiable matrix product states for simulating variational quantum computational chemistry
• Composite Quantum Phases in Non-Hermitian Systems
• The ITransverse.jl library for transverse tensor network contractions
• Dynamical Behaviour of Density Correlations Across the Chaotic Phase for Interacting Bosons