Eliminating the wave function singularity for ultracold atoms by 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 non-singular eigenfunctions are approximated by stochastic Fock-space diagonalisation 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.

arXiv comment16 pages, 11 figures; revised after referee comments

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• Improved walker population control for full configuration interaction quantum Monte Carlo
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity
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• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Compactification of Determinant Expansions via Transcorrelation
• TC++: First-principles calculation code for solids using the transcorrelated method
• Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian
• Scaling up the transcorrelated density matrix renormalization group
• Effective theory for strongly attractive one-dimensional fermions