The Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons: Theory, Implementation and Applications

TL;DR

The paper introduces ML-MCTDHB, a highly accurate, variational method for simulating quantum dynamics of bosonic systems, capable of handling complex multi-species and multi-dimensional configurations with improved efficiency.

Contribution

It presents the development, theoretical foundation, and implementation of ML-MCTDHB, a novel multi-layer approach for ab-initio quantum dynamics of bosons, including multi-species and mixed-dimensional systems.

Findings

Demonstrated superior performance in tunneling dynamics simulations

Accurately describes few- to many-body bosonic systems

Handles multi-species and mixed-dimensional configurations

Abstract

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab-initio method for studying the quantum dynamics and stationary properties of bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.