Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit

Authors
Okunishi, K Hieida, Y Akutsu, Y
Citation
K. Okunishi et al., Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit, PHYS REV E, 59(6), 1999, pp. R6227-R6230
Citations number
29
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
59
Issue
6
Year of publication
1999
Pages
R6227 - R6230
Database
ISI
SICI code
1063-651X(199906)59:6<R6227:UAEDOD>2.0.ZU;2-C
Abstract
We study the asymptotic behavior of the eigenvalue distribution of the corn er transfer matrix (M-CTM) and the density matrix (M-DM) in the density-mat rix renormalization group. We utilize the relationship MDM = M-CTM(4), whic h holds for noncritical systems in the thermodynamic limit. We derive the e xact and universal asymptotic form of the hl,M-DM eigenvalue distribution f or a class of integrable models in the massive regime. For nonintegrable mo dels, the universal asymptotic form is also verified by numerical renormali zation group calculations. [S1063-651X(99)50806-4].