Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium

TL;DR

This paper introduces a novel matrix-product-state method with dynamical local basis optimization to efficiently simulate the nonequilibrium dynamics of bosonic systems, capturing complex phenomena like self-trapping and dissipation.

Contribution

It combines the TEBD algorithm with a dynamical basis optimization, significantly reducing computational costs for large bosonic fluctuations in 1D correlated systems.

Findings

Accurately simulates nonequilibrium Holstein polarons

Reveals transient self-trapping phenomena

Demonstrates efficiency in scattering problems

Abstract

We present a method for simulating the time evolution of one-dimensional correlated electron-phonon systems which combines the time-evolving block decimation algorithm with a dynamical optimization of the local basis. This approach can reduce the computational cost by orders of magnitude when boson fluctuations are large. The method is demonstrated on the nonequilibrium Holstein polaron by comparison with exact simulations in a limited functional space and on the scattering of an electronic wave packet by local phonon modes. Our study of the scattering problem reveals a rich physics including transient self-trapping and dissipation.