Abstract
The method of correlated basis functions (CBF) is applied at the variational level to the transverse Ising model in two and three spatial dimensions (D=2,3). The model consists of Pauli spins arranged on a simple square or cubic lattice, experiencing nearest-neighbor interactions through their x components and subject to a transverse field in the z direction of strength λ. Working at zero temperature, full optimization of a Hartree-Jastrow trial wave function is performed by solving two Euler-Lagrange equations, namely a renormalized Hartree equation for the order parameter characterizing the ferromagnetic phase and a paired-magnon equation for the optimal two-spin spatial distribution function. The optimized trial wave function yields a second-order transition with a numerically determined critical coupling of λc=3.14(D=2) or λc= 5.10(D=3). Numerical results have been obtained for the magnetization order parameter, the energy per spin and its potential component, the static structure function at zero wave number, and the magnon energy gap corresponding to a Feynman description of the elementary excitations. Correlated density matrix theory provides for a natural extension of this approach to finite temperature.
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