The Chalker-Coddington Network Model is Quantum Critical

Details The Chalker-Coddington Network Model is Quantum Critical The Chalker-Coddington Network Model is Quantum Critical

1998-12-16

arxiv.org/abs/cond-mat/9812261v2

Phys. Rev. Lett. 82, 4906 - 4909 (1999)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Version accepted for publication in PRL. 4 pages, 2 eps figures

Scientific paper

10.1103/PhysRevLett.82.4906

We show that the localization transition in the integer quantum Hall effect as described by the Chalker-Coddington network model is quantum critical. We first map the anisotropic network model to the problem of diagonalizing a one-dimensional non-Hermitian non-compact supersymmetric lattice Hamiltonian of interacting bosons and fermions. Its behavior is investigated numerically using the density matrix renormalization group method, and critical behavior is found at the plateau transition. This result is confirmed by an exact, analytic, generalization of the Lieb-Schultz-Mattis theorem.

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