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Dukelsky, Mart\'in-Delgado, Nishino and Sierra (Europhys. Lett., 43, 457(1998) - hereafter referred to as DMNS) investigated the matrix product method(MPM), comparing it with the infinite-size density matrix renormalization group(DMRG). For equivalent basis size, the MPM produces an improved variationalenergy over that produced by DMRG and, unlike DMRG, produces atranslationally-invariant wavefunction. The DMRG results presented weresignificantly worse than the MPM, caused by a shallow bound state appearing atthe join of the two DMRG blocks. They also suggested that the DMRG results canbe improved by using an alternate superblock construction $[B] \bullet [B]$ forthe last few steps of the calculation. In this comment, we show that the DMRGresults presented by DMNS are in error and the artificial bound state producedby the standard superblock configuration is very small even for $m=2$ stateskept. In addition, we calculate explicitly the energy and wavefunction for the$[B] \bullet [B]$ superblock structure and verify that the energy coincideswith that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev.Lett., 75, 3537 (1995)).Comment: 2 pages, 1 eps figure included. eps.cls include

epl (europhysics letters)

Comment on “Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains” by J. Dukelsky <i>et al.</i>

Comment on “Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains” by J. Dukelsky et al.