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Exact diagonalization expansions of Bose or Fermi gases with contactinteractions converge very slowly due to a non-analytic cusp in the wavefunction. Here we develop a transcorrelated approach where the cusp is treatedexactly and folded into the many-body Hamiltonian with a similaritytransformation that removes the leading order singularity. The resultingtranscorrelated Hamiltonian is not hermitian but can be treated numericallywith a standard projection approach. The smoothness of the wave functionimproves by at least one order and thus the convergence rate for the groundstate energy improves. By numerical investigation of a one-dimensional gas ofspin-$\frac{1}{2}$ fermions we find the error in the transcorrelated energy toscale as $M^{-3}$ with a single-particle basis of $M$ plane waves compared to$M^{-1}$ for the expansion of the original Hamiltonian and $M^{-2}$ usingconventional lattice renormalization.

Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions