Marshall’s sign rule and density-matrix renormalization-group acceleration

Abstract

In applications of White's density-matrix renormalization-group (DMRG) algorithm, computation time is dominated by the diagonalization of large sparse Hamiltonians by iterative diagonalization algorithms, whose convergence can be decisively accelerated by the usage of good start vectors. In this paper I show how, using the Marshall sign rule, in a wide class of antiferromagnetic models the number of diagonalization iterations can be reduced below 10, sometimes down to 2, accelerating the DMRG by an order of magnitude. This acceleration, applicable during the growth of long chains, complements the acceleration procedure proposed by White. To illustrate the feasibility of the approach, I show how it performs if applied to the calculation of the Haldane gap for $S=2.$