Density-matrix renormalization group for a gapless system of free fermions

We investigate convergence of the density-matrix renormalization group (DMRG) in the thermodynamic limit for gapless systems. Although the DMRG correlations always decay exponentially in the thermodynamic limit, the correlation length at the DMRG fixed-point scales as xi similar to m(1.3), where in is the number of kept states, indicating the existence of algebraic order for the exact system. The single-particle excitation spectrum is calculated, using a Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the symmetry E(k)=E(pi-k) for translationally invariant half-integer spin-systems with local interactions. Finally, we provide a method to compute overlaps between ground states obtained from different DMRG calculations. [S0163-1829(99)05315-1].