Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via nonunitary similarity transformations

© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Similarity transformation of the Hubbard Hamiltonian using a Gutzwiller correlator leads to a non-Hermitian effective Hamiltonian, which can be expressed exactly in momentum-space representation and contains three-body interactions. We apply this methodology to study the two-dimensional Hubbard model with repulsive interactions near half filling in the intermediate interaction strength regime (U/t=4). We show that at optimal or near optimal strength of the Gutzwiller correlator, the similarity-transformed Hamiltonian has extremely compact right eigenvectors, which can be sampled to high accuracy using the full configuration interaction quantum Monte Carlo (FCIQMC) method and its initiator approximation. Near-optimal correlators can be obtained using a simple projective equation, thus obviating the need for a numerical optimization of the correlator. The FCIQMC method, as a projective technique, is well suited for such non-Hermitian problems, and its stochastic nature can handle the three-body interactions exactly without undue increase in computational cost. The highly compact nature of the right eigenvectors means that the initiator approximation in FCIQMC is not severe and that large lattices can be simulated, well beyond the reach of the method applied to the original Hubbard Hamiltonian. Results are provided in lattice sizes up to 50 sites and compared to auxiliary-field QMC. New benchmark results are provided in the off-half-filling regime, with no severe sign problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations

Similarity transformation of the electronic Schrödinger equation via Jastrow factorization

By expressing the electronic wavefunction in an explicitly correlated (Jastrow-factorized) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits the use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionization potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort

Similarity transformation of the electronic Schrödinger equation via Jastrow factorization

© 2019 Author(s). By expressing the electronic wavefunction in an explicitly correlated (Jastrow-factorized) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits the use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionization potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort

NECI: N-Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green’s functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0