FCIQMC

Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a stochastic projector method for solving the electronic Schrödinger equation within the full configuration interaction (CI) space. It represents the many-electron wavefunction as a linear combination of Slater determinants in a chosen one-electron basis, and samples the coefficients with a population of signed walkers. The method was introduced by Garnet K. Booth, Andrew J. W. Thom, and N. C. Handy? Wait, the names: Booth, Thom, and Alavi in 2009, and has since been developed further.

In FCIQMC, the imaginary-time evolution of the determinant amplitudes follows the action of the Hamiltonian matrix in the determinant basis. The simulation proceeds with spawning moves where walkers attempt to populate connected determinants based on off-diagonal Hamiltonian elements, as well as death or birth steps driven by diagonal elements. Walkers on the same determinant with opposite signs annihilate each other, which helps manage the fermionic sign problem. A global shift parameter is used to control the overall population, and energy estimates for the ground state are obtained from this shift or from projected estimators as the simulation converges.

A key development is the initiator approximation (i-FCIQMC), which designates determinants with sufficiently large walker populations as initiators. Initiators are allowed to spawn to new determinants, while non-initiators have restricted spawning. This reduces noise and accelerates convergence with fewer walkers; exact results are recovered in the limit of large walker populations or with corrective schemes.

FCIQMC has enabled sampling of very large CI spaces and has been applied to challenging strongly correlated systems and potential energy surfaces. It remains computationally demanding and sensitive to basis choice, convergence criteria, and the management of sign structure, but it provides a controllable route to near-exact ground-state energies in systems inaccessible to conventional configuration-interaction methods.