Parity, precision and spin inversion within the density matrix renormalization group

Abstract

A way of implementing the density matrix renormalization group (DMRG) method which simplifies the use of real-space parity as a conserved quantum number is discussed. The use of parity in the infinite-system DMRG calculations is often necessary in order to calculate more than the lowest excitation gap in a system. In addition, the use of parity reduces the computational overhead by a factor of two. Using parity as a symmetry we give numerical evidence that the infinite-system DMRG method in some cases displays a power-law convergence with the number of states retained. In particular we show that the often-used measure of the error in a DMRG calculation, , bears only a marginal resemblance to the true error. Spin inversion is shown to be a very useful symmetry when performing calculations in the subspace, allowing for a distinction between even and odd multiplets even when using the finite-system method.