Variational Wave Functions and Parent Hamiltonians

Abstract

We do not know the ground state for most nonferromagnetic Heisenberg models. Even those that are known in analytical form, such as the Bethe solution in one dimension, require numerical computations for their spin correlations. Variational wave functions provide educated guesses for the ground state. Physical insight can be gained by a variational calculation, where the energy is minimized with respect to a chosen set of parameters. The variational approach takes us beyond the regimes of any particular expansion scheme—semiclassical, large N, or others. As shown for the Hubbard model (see Section 4.1), the primary advantage of the variational approach is that it is conceptuallly simple and clear.