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Simulating strongly correlated multiparticle systems in a truncated Hilbert space

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.