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

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.