Time evolution algorithms for Matrix Product States and DMRG

TL;DR

This paper introduces new algorithms for simulating 1D quantum systems using Matrix Product States, demonstrating that the Arnoldi method outperforms previous techniques in accuracy and efficiency, and applying it to study correlation transfer in cold atom systems.

Contribution

The paper develops and compares new time evolution algorithms for MPS, highlighting the superior performance of the Arnoldi method for 1D quantum simulations.

Findings

Arnoldi method achieves high accuracy with moderate resources.

Comparison shows Arnoldi outperforms Taylor and Padé approximations.

Application to Feshbach resonance reveals correlation transfer dynamics.

Abstract

In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pad\'e and Arnoldi approximations to the evolution operator. By comparing with previous techniques based on MPS and DMRG we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying how correlations are transferred from the atomic to the molecular cloud when crossing a Feschbach resonance with two-species hard-core bosons in a 1D optical lattice.