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Europhysics Letters (EPL)

Reply to the Comment by P. McCulloch and M. Gulácsi on “Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains”

J. Dukelsky, Miguel Angel Martin-Delgado, Tomotoshi Nishino, Tatsuaki Wada, Germán Sierra

Published Jan 1, 2003• 0 citations
Publisher
DOI
10.1209/epl/i2003-00327-4

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

Ian P. McCulloch, M. Gulácsi

Dukelsky, Martín-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 variational energy over that produced by DMRG and, unlike DMRG, produces a translationally-invariant wavefunction. The DMRG results presented were significantly worse than the MPM, caused by a shallow bound state appearing at the join of the two DMRG blocks. They also suggested that the DMRG results can be improved by using an alternate superblock construction $[B] \bullet [B]$ for the last few steps of the calculation. In this comment, we show that the DMRG results presented by DMNS are in error and the artificial bound state produced by the standard superblock configuration is very small even for $m=2$ states kept. In addition, we calculate explicitly the energy and wavefunction for the $[B] \bullet [B]$ superblock structure and verify that the energy coincides with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev. Lett., 75, 3537 (1995)).

arXiv:cond-mat/0210512•Europhysics Letters (EPL)•Jan 1, 2003•0 citations

New exact results on density matrix for XXX spin chain

T. Miwa, Fedor Aleksandrovich Smirnov

arXiv:1802.08491•Letters in Mathematical Physics•Dec 17, 2018•17 citations
Dukelsky, Martín-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 variational energy over that produced by DMRG and, unlike DMRG, produces a translationally-invariant wavefunction. The DMRG results presented were significantly worse than the MPM, caused by a shallow bound state appearing at the join of the two DMRG blocks. They also suggested that the DMRG results can be improved by using an alternate superblock construction [B]∙[B][B] \bullet [B][B]∙[B] for the last few steps of the calculation. In this comment, we show that the DMRG results presented by DMNS are in error and the artificial bound state produced by the standard superblock configuration is very small even for m=2m=2m=2 states kept. In addition, we calculate explicitly the energy and wavefunction for the [B]∙[B][B] \bullet [B][B]∙[B] superblock structure and verify that the energy coincides with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev. Lett., 75, 3537 (1995)).