Simulating strongly correlated multiparticle systems in a truncated Hilbert space

TL;DR

This paper introduces a rescaling method for contact interactions in finite basis representations of strongly correlated multi-particle systems, significantly improving the accuracy of numerical simulations of ultracold atoms.

Contribution

The paper derives an exact rescaling formula for two-particle systems and demonstrates its effectiveness in enhancing numerical accuracy for systems with up to five particles.

Findings

Rescaling improves ground state energy calculations.

Enhanced accuracy in excitation spectra and correlation functions.

Applicable to various external potentials.

Abstract

Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. Detailed comparison between finite Hilbert space calculations and exact results for up to 5 particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground state energies, the low-lying excitation spectrum, density profile and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.