Eliminating the wave-function singularity for ultracold atoms by a similarity transformation
Abstract
A hyperbolic singularity in the wave function of s -wave interacting atoms is the root problem for any accurate numerical simulation. Here, we apply the transcorrelated method, whereby the wave-function singularity is explicitly described by a two-body Jastrow factor, and then folded into the Hamiltonian via a similarity transformation. The resulting nonsingular eigenfunctions are approximated by stochastic Fock-space diagonalization with energy errors scaling with 1 /M in the number M of single-particle basis functions. The performance of the transcorrelated method is demonstrated on the example of strongly correlated fermions with unitary interactions. The current method provides the most accurate ground-state energies so far for three and four fermions in a rectangular box with periodic boundary conditions.
- Publication:
-
Physical Review Research
- Pub Date:
- November 2020
- DOI:
- 10.1103/PhysRevResearch.2.043270
- arXiv:
- arXiv:2002.05987
- Bibcode:
- 2020PhRvR...2d3270J
- Keywords:
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- Condensed Matter - Quantum Gases
- E-Print:
- 16 pages, 11 figures