Density-matrix renormalization-group algorithm for quantum lattice systems with a large number of states per site

A variant of White's density-matrix renormalization-group scheme, which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models-the spin-1/2 antiferromagnetic Heisenberg chain and a dimerized XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings that are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.