Density Matrix and Renormalization for Classical Lattice Models

TL;DR

This paper reviews the application of the density matrix renormalization group (DMRG) method to classical lattice models, emphasizing the variational principle and the use of corner transfer matrices for 2D models.

Contribution

It introduces a novel application of DMRG to 2D classical lattice models using corner transfer matrices, expanding the method's scope.

Findings

DMRG maximizes an approximate partition function.

Application of DMRG to 2D models via CTMs.

Discussion of future directions in DMRG research.

Abstract

We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state energy. The variational principle is applied to two-dimensional (2D) classical lattice models, where the density matrix is expressed as a product of corner transfer matrices. (CTMs) DMRG related fields and future directions of DMRG are briefly discussed.