Improved Hamiltonian variational technique for lattice models

In the context of the Hamiltonian variational approach we propose a systematic method for the improvement of any given trial wave function. The approach has many similarities with the Lanczos scheme and it may be used for quantum-mechanical problems as well as field-theory and statistical-mechanics systems. We apply the method to the Mathieu equation and to the Ising one-dimensional model in a finite lattice. The agreement between our results and the exact ones is excellent in the whole range of parameters. We also briefly discuss the application of these ideas to lattice gauge theories and the similarities with other recently proposed methods.