Time evolution of Matrix Product States

TL;DR

This paper introduces new algorithms for simulating 1D quantum systems using Matrix Product States combined with Taylor, Pade, and Arnoldi methods, showing Arnoldi's superior accuracy and applying it to molecule formation in optical lattices.

Contribution

It develops and compares novel simulation algorithms for quantum dynamics, highlighting the effectiveness of the Arnoldi method over existing Trotter-based techniques.

Findings

Arnoldi method achieves higher accuracy with moderate resources.

Compared methods demonstrate Arnoldi's superiority over Trotter decompositions.

Application to molecule formation in optical lattices illustrates practical utility.

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, Pade and Arnoldi approximations to the evolution operator. By comparing all methods with previous techniques based on Trotter decompositions we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying the formation of molecules in an optical lattices when crossing a Feschbach resonance with a cloud of two-species hard-core bosons.