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Progress of Theoretical Physics Supplement

Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method(Interaction and Nanostructural Effects in Low-Dimensional Systems)

Naokazu Shibata

Published Feb 5, 2009• 0 citations
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The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at ν= 2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor ν= 1.

arXiv:0906.1036•Progress of Theoretical Physics Supplement•Jan 1, 2008•9 citations
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.
The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at ν= 2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor ν= 1.