Parallel time-dependent variational principle algorithm for matrix product states

TL;DR

This paper introduces a parallel time-dependent variational principle algorithm for matrix product states, enabling efficient simulation of long-range interacting 1D quantum systems with high scalability and accuracy.

Contribution

It presents the first parallel TDVP algorithm for MPS that effectively handles long-range interactions and demonstrates high parallel efficiency and applicability to complex many-body systems.

Findings

Scales well up to 32 processes with 86% efficiency.

Accurately simulates quenches in long-range Ising and XY models.

Calculates dynamical correlations in a 201-site Heisenberg chain.

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 $1/r^2$ interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.