BeveridgeAnsatz

BeveridgeAnsatz is a family of variational wavefunction forms used in quantum many-body theory to approximate ground and excited states. The central idea is to start from a simple reference state, such as a Slater determinant in fermionic systems or a mean-field product state, and to apply a correlation operator that injects interparticle correlations. The resulting state can be written as |Ψ⟩ = Cβ |Φ0⟩, where Cβ is a parametrized operator or function depending on variational parameters β. Common realizations include multiplicative correlation factors (such as a Jastrow-type function) acting on the reference state, or more general operators that modify amplitudes and phases of configurations.

Applications: The Beveridge Ansatz has been discussed in contexts including quantum chemistry for capturing dynamical and static correlation, condensed-matter models of strongly correlated electrons, nuclear structure, and ultracold atomic systems. It is often optimized by variational methods, sometimes in combination with Monte Carlo sampling, to minimize the energy or to study properties beyond mean-field theory.

Advantages: It provides a flexible framework with systematic improvability by including additional correlation terms, and can preserve or break specific symmetries as needed. It can interpolate between mean-field descriptions and more correlated wavefunctions.

Limitations: The effectiveness depends on the choice of reference state and the form of Cβ; the parameter space can be large and difficult to optimize; computational cost grows with the complexity of the correlation operator; enforcing exact symmetries or size-consistency can be nontrivial.

See also: Ansätze, variational method, Jastrow factor, tensor network states, coupled-cluster theory.