The Projector Expansion Method in Hamiltonian Lattice Systems.
Abstract
Encouraging developments in the projector expansion method, or texpansion, of Horn and Weinstein are presented. This method uses the operator e^{tH} to project trial states onto the lowlying eigenstates of a Hamiltonian H. Estimates of expectation values are obtained through a process of power series expansion and subsequent series analysis. Although the method is a nonperturbative computational scheme for general Hamiltonian systems, it is particularly wellsuited to systems defined on a lattice. A technique for exactly computing texpansion coefficients in infinite lattice systems is described. This technique is a modification of the finite cluster method of Domb from statistical mechanics and is much simpler to implement than previouslyused methods, facilitating the evaluation of higherorder terms in the expansions. The number of terms obtained in several of the series considered here is significantly greater than in any previous texpansion study. This method can also be easily used in the calculation of expansion coefficients in the bistate contraction scheme. Several methods of series analysis are examined and a simple procedure for testing the reliability of the extrapolations is suggested. The first investigation of a lattice gauge theory using the bistate contraction is presented. The effectiveness of this scheme in determining the values of physical quantities in the continuum limit is demonstrated. The projector expansion method with bistate contraction is applied to two lattice models: the anisotropic Heisenberg antiferromagnetic chain and the compact formulation of U(1) Hamiltonian lattice gauge theory in 2 + 1 dimensions. In the former, the ground state energy, nearestneighbour longitudinal spinspin correlation function, and the triplet singlet gap are studied. In the latter, the ground state energy, mean plaquette, specific heat, photon mass, and the mass gap in the vacuum sector (the socalled glueball mass) are investigated. The results confirm that this lattice theory has only a single confining phase. No evidence of a stable glueball in the vacuum sector is found in the continuum limit.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......274M
 Keywords:

 Physics: General