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Updated: Aug 18, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic
K Okunishi1, Y Hieida, Y Akutsu
1Department of Physics, Graduate School of Science, Osaka University, Machikaneyama-cho 1-1, Toyonaka, Osaka 560-0043, Japan.
Abstract:
We study the asymptotic behavior of the eigenvalue distribution of the corner transfer matrix (M(CTM)) and the density matrix (M(DM)) in the density-matrix renormalization group. We utilize the relationship M(DM)=M(4)(CTM), which holds for noncritical systems in the thermodynamic limit. We derive the exact and universal asymptotic form of the M(DM) eigenvalue distribution for a class of integrable models in the massive regime. For nonintegrable models, the universal asymptotic form is also verified by numerical renormalization group calculations.
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