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A variant of White's density matrix renormalisation group scheme which isdesigned to compute low-lying energies of one-dimensional quantum latticemodels with a large number of degrees of freedom per site is described. Themethod is tested on two exactly solvable models---the spin-1/2antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustratethe potential of the method, it is applied to a model of spins interacting withquantum phonons. It is shown that the method accurately resolves a number ofenergy gaps on periodic rings which are sufficiently large to afford anaccurate investigation of critical properties via the use of finite-sizescaling theory.Comment: RevTeX, 8 pages, 2 figure

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