Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

2003/09/02 by Naokazu Shibata
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Density matrix #Density matrix renormalization group #Eigenvalues and eigenvectors #Matrix (chemical analysis) #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum system #Transfer matrix #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1088/0305-4470/36/37/201

published as J. Phys. A: Math. Gen. vol.36 (2003) R381 · 33 pages, 18 figures; corrected Eq.(117)

openalex publication_date 2003/09/02 · arxiv created 2003/11/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground-state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to two-dimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.

Citations

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