ESTIMATION OF PROPERTIES OF LOW-LYING EXCITED-STATES OF HUBBARD MODELS - A MULTICONFIGURATIONAL SYMMETRIZED PROJECTOR QUANTUM MONTE-CARLO APPROACH

We present in detail the recently developed multiconfigurational symme trized projector quantum Monte Carlo method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo metho d for a multiconfigurational trial wave function. We give a detailed d iscussion of issues related to the symmetry of the projection procedur e that validates our Monte Carlo procedure for excited states. In this context we discuss various averaging procedures for the Green functio n and present an analysis of the errors incurred in these procedures. We study the ground-state energy and correlation functions of the one- dimensional Hubbard model at half-tilling to confirm these analyses. W e then study the energies and correlation functions of excited states of Hubbard chains. Hubbard rings away from half-filling are also studi ed and the pair binding energies for holes of 4n and 4n + 2 systems ar e compared with the Bethe ansatz results of Fye, Martins, and Scaletta r [Phys. Rev. B 42, 6809 (1990)]. Our study of the two-dimensional Hub bard model includes the 4x2 ladder and the 3x3 lattice with periodic b oundary conditions. The 3x4 lattice is nonbipartite and amenable to ex act diagonalization studies and is, therefore, a good candidate for ch ecks on the method. We are able to reproduce accurately the energies o f ground and excited states, both at and away from half-filling. We st udy the properties of the 4x2 Hubbard ladder with bond alternation as the correlation strength and filling are varied. The method reproduces the correlation functions accurately. We also examine the severity of sign problem for one-and two-dimensional systems.