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

REVIEW ARTICLE

Naokazu Shibata

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TOPICAL REVIEW

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.


PACS

02.60.Dc Numerical linear algebra

02.10.Ud Linear algebra

73.43.Cd Theory and modeling

MSC

81V70 Many-body theory; quantum Hall effect

65F15 Eigenvalues, eigenvectors

Subjects

Mathematical physics

Computational physics

Surfaces, interfaces and thin films

Dates

Issue 37 (19 September 2003)

Received 27 March 2003, in final form 9 June 2003

Published 2 September 2003



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