Universal Asymptotic Eigenvalue Distribution of Density Matrices and the Corner Transfer Matrices in the Thermodynamic Limit

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dc.creatorOkunishi, Kouichi
dc.creatorHieida, Yasuhiro
dc.creatorAkutsu, Yasuhiro
dc.date1998-10-20
dc.date.accessioned2026-07-07T06:34:02Z
dc.date.available2026-07-07T06:34:02Z
dc.descriptionWe study the asymptotic behavior of the eigenvalue distribution of the Baxter's corner transfer matrix (CTM) and the density matrix (DM) in the White's density-matrix renormalization group (DMRG), for one-dimensional quantum and two-dimensional classical statistical systems. We utilize the relationship ${\rm DM}={\rm CTM}^4$ which holds for non-critical systems in the thermodynamic limit. Using the known diagonal form of CTM, we derive exact asymptotic form of the DM eigenvalue distribution for the integrable $S=1/2$ XXZ chain (and its related integrable models) in the massive regime. The result is then recast into a ``universal'' form without model-specific quantities, which leads to $ω_{m}\sim \exp[-{\rm const.}(\log m)^2]$ for $m$-th DM eigenvalue at larg $m$. We perform numerical renormalization group calculations (using the corner-transfer-matrix RG and the product-wavefunction RG) for non-integrable models, verifying the ``universal asymptotic form'' for them. Our results strongly suggest the universality of the asymptotic eigenvalue distribution of DM and CTM for a wide class of systems.
dc.description4 pages, RevTeX, 4 ps figures
dc.identifierhttps://arxiv.org/abs/cond-mat/9810239
dc.identifierhttp://arxiv.org/abs/cond-mat/9810239
dc.identifierPhys. Rev. E 59 R6227 (1999)
dc.identifierdoi:10.1103/PhysRevE.59.R6227
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99396
dc.subjectStatistical Mechanics
dc.titleUniversal Asymptotic Eigenvalue Distribution of Density Matrices and the Corner Transfer Matrices in the Thermodynamic Limit
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