Abstract
Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a nonanalytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded into the many-body Hamiltonian with a similarity transformation that removes the leading-order singularity. The resulting transcorrelated Hamiltonian is not Hermitian but can be treated numerically with a standard projection approach. The smoothness of the wave function improves by at least one order and thus the convergence rate for the ground-state energy improves. By numerical investigation of a one-dimensional gas of spin- fermions we find the error in the transcorrelated energy to scale as with a single-particle basis of plane waves compared to for the expansion of the original Hamiltonian and using conventional lattice renormalization.
9 More- Received 20 August 2018
DOI:https://doi.org/10.1103/PhysRevA.98.053627
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