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Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
Péter Jeszenszki, Hongjun Luo, Ali Alavi, Joachim Brand
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Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a non-analytic 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-1/2 fermions we find the error in the transcorrelated energy to scale 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 using conventional lattice renormalization.
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