Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction

Journal Article · Mon Nov 15 04:00:00 EST 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2021.168592· OSTI ID:23183198

Gwak, Yeongjin ^[1]; Marchukov, Oleksandr V. ^[2]

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1. Center for Theoretical Physics, Department of Physics and Astronomy, Seoul National University, 08826, Seoul (Korea, Republic of)
2. Technische Universität Darmstadt, Institut für Angewandte Physik, 64289 Darmstadt (Germany)

Highlights: • Comparison of exact and numerical single-particle density matrices. • Benchmark for multiconfigurational Hartree. • Convergence for large number of orbitals. We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, as well as overestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

• OSTI ID: 23183198
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 434; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BENCHMARKS
BOSE-EINSTEIN GAS
BOSONS
DENSITY MATRIX
EXACT SOLUTIONS
GROUND STATES
HARMONICS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
SCATTERING LENGTHS
TIME DEPENDENCE
WAVE FUNCTIONS