Chebyshev matrix product state approach for time evolution

Abstract

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the non-projective method and more efficient information storage, data compression, and less computational effort.

14 pages, 8 figures

References in corpus (20)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The Kernel Polynomial Method
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Matrix product states represent ground states faithfully
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Time-evolving a matrix product state with long-ranged interactions
• Time-step targetting methods for real-time dynamics using DMRG
• Time evolution algorithms for Matrix Product States and DMRG
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Chebyshev matrix product state approach for spectral functions
• Controlling and Detecting Spin Correlations of Ultracold Atoms in Optical lattices
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Chebyshev expansion for Impurity Models using Matrix Product States
• Time evolution of one-dimensional Quantum Many Body Systems
• Spectral functions and time evolution from the Chebyshev recursion
• Matrix product state formulation of frequency-space dynamics at finite temperatures
• Numerical evaluation of Greens functions based on the Chebyshev expansion

Cited by in corpus (21)

• Time-evolution methods for matrix-product states
• Lecture Notes of Tensor Network Contractions
• Numerical Assessment for Accuracy and GPU Acceleration of TD-DMRG Time Evolution Schemes
• Performance of the time-dependent variational principle for matrix product states in long-time evolution of a pure state
• Topological spin excitations in Harper-Heisenberg spin chains
• Probing thermalization through spectral analysis with matrix product operators
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• How much entanglement is needed to reduce the energy variance?
• Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations
• Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
• Dynamic structure factor of the spin-1/2 XXZ chain in a transverse field
• Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
• Approximating the long time average of the density operator: Diagonal ensemble
• Root-N Krylov-space correction-vectors for spectral functions with the density matrix renormalization group
• Initial State Dependent Dynamics Across Many-body Localization Transition
• Dynamical correlation functions from complex time evolution
• Density of States of the lattice Schwinger model
• Matrix Product States with adaptive global symmetries
• Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Sudden quench of harmonically trapped mass-imbalanced fermions