Dynamics of Hubbard Hamiltonians with the multiconfigurational time-dependent Hartree method for indistinguishable particles

TL;DR

This paper applies the MCTDH-X method to simulate the dynamics of bosons and fermions in Hubbard models, demonstrating its accuracy and exploring correlation buildup during condensate splitting in lattices.

Contribution

The paper introduces the application of the multiconfigurational time-dependent Hartree method for indistinguishable particles to Hubbard Hamiltonians, including derivation of equations of motion and validation against exact solutions.

Findings

MCTDH-X accurately reproduces exact diagonalization results.

Correlation buildup depends on ramping time during condensate splitting.

Fast ramps can lead to coherence revivals.

Abstract

We apply the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) to systems of bosons or fermions in lattices described by Hubbard type Hamiltonians with long-range or short-range interparticle interactions. The wavefunction is expanded in a variationally optimized time-dependent many-body basis generated by a set of effective creation operators that are related to the original particle creation operators by a time-dependent unitary transform. We use the time-dependent variational principle for the coefficients of this transform as well as the expansion coefficients of the wavefunction in the time-dependent many-body basis as variational parameters to derive equations of motion. The convergence of MCTDH-X is shown by comparing its results to the exact diagonalization of one-, two-, and three-dimensional lattices filled with bosons with contact interactions. We use MCTDH-X to study the buildup of correlations in the long-time splitting dynamics of a Bose-Einstein condensate loaded into a large two-dimensional lattice subject to a barrier that is ramped up in the center. We find that the system is split into two parts with emergent time-dependent correlations that depend on the ramping time -- for most barrier-raising-times the system becomes two-fold fragmented, but for some of the very fast ramps, the system shows revivals of coherence.