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We introduce nested gausslet bases, an improvement on previous gausslet bases that can treat systems containing atoms with much larger atomic numbers. We also introduce pure Gaussian distorted gausslet bases, which allow the Hamiltonian integrals to be performed analytically, as well as hybrid bases in which the gausslets are combined with standard Gaussian-type bases. All these bases feature the diagonal approximation for the electron–electron interactions so that the Hamiltonian is completely defined by two Nb × Nb matrices, where Nb ≈ 104 is small enough to permit fast calculations at the Hartree–Fock level. In constructing these bases, we have gained new mathematical insight into the construction of one-dimensional diagonal bases. In particular, we have proved an important theorem relating four key basis set properties: completeness, orthogonality, zero-moment conditions, and diagonalization of the coordinate operator matrix. We test our basis sets on small systems with a focus on high accuracy, obtaining, for example, an accuracy of 2 × 10−5 Ha for the total Hartree–Fock energy of the neon atom in the complete basis set limit.
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This content will become publicly available on October 1, 2026
Scaling up the transcorrelated density matrix renormalization group
Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their application to larger systems has been hampered by the computational cost. We develop improved techniques for the transcorrelated density-matrix renormalization group (DMRG), in which the ground state of the transcorrelated Hamiltonian is represented as a matrix product state (MPS), and demonstrate large-scale calculations of the ground-state energy of the two-dimensional Fermi-Hubbard model. Our developments stem from three technical inventions: (i) constructing matrix product operators (MPOs) of transcorrelated Hamiltonians with low bond dimension and high sparsity, (ii) exploiting the entanglement structure of the ground states to increase the accuracy of the MPS representation, and (iii) optimizing the nonlinear parameter of the Gutzwiller correlator to mitigate the nonvariational nature of the transcorrelated method. We examine systems of size up to 12×12 lattice sites, four times larger than previous transcorrelated DMRG studies, and demonstrate that transcorrelated DMRG yields significant improvements over standard nontranscorrelated DMRG for equivalent computational effort. Transcorrelated DMRG reduces the error of the ground-state energy by 2.4×–14×, with the smallest improvement seen for a small system at half filling and the largest improvement in a dilute closed-shell system.
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- Award ID(s):
- 2037832
- PAR ID:
- 10645501
- Publisher / Repository:
- APS
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 112
- Issue:
- 16
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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