Comments on variational ground states for lattice hamiltonians

Yang Zhao

Bibhas Bhattacharyya

The variational principle is revisited in the context of finding the upper and lower bounds to the ground state energy. It is shown how the variational principle can be employed to find the lower bound by partitioning the Hamiltonian into several parts. We demonstrate how the variational principle can be used to find the exact ground states in some special cases. We consider the harmonic oscillator and the Ising Hamiltonian on a bipartite lattice which are familiar yet instructive examples for students.

D O'Shaughnessy, Conrad J. Burden

Estimates of the ground state wavefunction of (2+ 1 )-dimensional non-compact U (1) Hamiltonian lattice gauge theory are found in terms of variational wavefunctions with up to four parameters. These wavefunctions are compared with the exact ground state as a test of the accuracy of the method.

Zhengqian Cheng, Chris A. Marianetti

Samuel P. Bowen, Jay D. Mancini

A variational calculation of the ground state of the Anderson lattice model is discussed. The calculation creates a finite Hamiltonian matrix for many-electron states, which are appropriate for the thermodynamic limit. A simple 14×14 truncation is discussed for finite U and a smaller 3×3 is used for the large U limit. Both approximations indicate that the spin configurations of the localized f orbitals are antiferromagnetically correlated for nearest neighbors in the ground state. This antiferromagnetic correlation is mediated by an RKKY interaction and thus offers a variety of spin orderings as a function of lattice and density.

V. Tarasov, Leon Armenovich Takhtadzhyan, L. D. Faddeev