Density Matrix and Renormalization for Classical Lattice Models

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.

21 pages, Latex, 14 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems"

References in corpus (11)

• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Corner Transfer Matrix Renormalization Group Method
• Density Matrix Renormalization Group Method for 2D Classical Models
• Density-matrix renormalization-group method in momentum space
• Product Wave Function Renormalization Group Method
• Numerical Renormalization Group at Criticality
• Spin and charge gaps in the one-dimensional Kondo-lattice model with Coulomb interaction between conduction electrons
• Analytic Formulations of the Density Matrix Renormalization Group
• Density Matrix Renormalization Group Study of the Spin 1/2 Heisenberg Ladder with Antiferromagnetic Legs and Ferromagnetic Rungs
• The Correlated Block Renormalization Group

Cited by in corpus (7)

• Entanglement Entropy and Quantum Field Theory
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Negativity spectrum in 1D gapped phases of matter
• Corrections to scaling for block entanglement in massive spin-chains
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Numerical Latent Heat Observation of the q=5 Potts Model