Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring

Abstract

We develop a method to describe the temporal evolution of an interacting system of bosons, for which the field operator expansion is truncated after a finite number $M$ of modes, in a rigorously controlled manner. Using McLachlan's principle of least error, we find a self-consistent set of equations for the many-body state. As a particular benefit, and in distinction to previously proposed approaches, the presently introduced method facilitates the dynamical increase of the number of orbitals during the temporal evolution, due to the fact that we can rigorously monitor the error made by increasing the truncation dimension $M$. The additional orbitals, determined by the condition of least error of the truncated evolution relative to the exact one, are obtained from an initial trial state by steepest $constrained$ descent.

12 pages of RevTex4-1

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• Dynamical pruning of the multiconfiguration time-dependent Hartree method (DP-MCTDH): An efficient approach for multidimensional quantum dynamics
• Center-of-mass motion as a sensitive convergence test for variational multi-mode quantum dynamics
• Local-in-time error in variational quantum dynamics
• "Photonic" cat states from strongly interacting matter waves
• Self-consistent many-body metrology
• Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap
• Exact variational dynamics of the multimode Bose-Hubbard model based on SU(M) coherent states
• Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction