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.

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We investigate the ground-state wave function of a prototypical strongly correlated system, a three-band (p-d) Hubbard model of cuprates, using full configuration interaction quantum Monte Carlo. We show that the configuration interaction description of the exact ground state wave function is profoundly affected by the choice of single-particle representation, in a counterintuitive manner. Thus a broken-symmetry unrestricted Hartree-Fock basis, which at a single configuration level produces a qualitatively correct description of the antiferromagnet, results in a highly entangled exact solution consisting of high particle-hole excitations of the reference. This wave function is found to be very difficult to approximate using subspace diagonalizations. Conversely, a restricted Hartree-Fock basis, which yields at a single configuration level a qualitatively incorrect paramagnetic metal, results in a relatively rapidly converging configuration interaction expansion. Convergence can be further accelerated by adopting a natural orbital representation. Our results suggest that with the correct single-particle basis, such strongly correlated systems may be described by relatively compact wave functions.

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