LewisAnsatz

The LewisAnsatz is a variational wavefunction approach used in quantum many-body physics and quantum chemistry to approximate the ground state of interacting particles. It seeks to balance accuracy with computational efficiency by combining a reference structure with an explicit correlation factor.

Typically, the ansatz takes the form Psi_L = F(r_1,...,r_N) * Phi_0, where Phi_0 is a mean-field reference such as a Slater determinant (for fermions) or a product state (for bosons), and F is a symmetry-respecting correlation factor that depends on interparticle coordinates and possibly spin. The correlation factor is often chosen to resemble a Jastrow-type function or a product of pairwise terms, enabling explicit incorporation of short-range correlations beyond mean-field.

Parameters in F and the orbitals composing Phi_0 are optimized variationally to minimize the expectation value of the Hamiltonian. The LewisAnsatz thus provides a flexible framework that can interpolate between mean-field theories and more exact stochastic or configuration-interaction methods, while typically requiring less computational resources than full CI or coupled-cluster calculations.

Applications of the LewisAnsatz span electronic structure calculations in molecules, lattice models in condensed matter physics, and, more generally, any system where correlation effects play a significant role but full configuration interaction is impractical. Its performance depends on the choice of correlation factor and the quality of the reference state.

Limitations of the LewisAnsatz include potential lack of size consistency, dependence on the chosen functional form, and challenges in efficiently optimizing large parameter sets. It is often used in conjunction with stochastic methods such as variational Monte Carlo or diffusion Monte Carlo to evaluate energies. Related approaches include Hartree-Fock, Jastrow factors, and other ansatz-based methods.