Integrable modification of the critical Chalker-Coddington network model

Article

关键词: QUANTUM HALL TRANSITION;    2 DIMENSIONS;    MAGNETIC-FIELD;    ANTIFERROMAGNETIC CHAIN;    CRITICAL-POINT;    RSOS MODELS;    LATTICE;    PERCOLATION;    ALGEBRA;    DELOCALIZATION;   

DOI  :  10.1103/PhysRevB.84.144201

来源: SCIE

【 摘 要 】

We consider the Chalker-Coddington network model for the integer quantum Hall effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models with two loop flavors. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra and parameterized by the loop fugacity n. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-gas theory, whereas the other two branches (3,4) couple the two loop flavors, and relate to an SU(2)(r) x SU(2)(r)/SU(2)(2r) Wess-Zumino-Witten (WZW) coset model for the particular values n = -2 cos[pi/(r + 2)], where r is a positive integer. The truncated Chalker-Coddington model is the n = 0 point of branch 4. By numerical diagonalization, we find that its universality class is neither an analytic continuation of the WZW coset nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.

【 授权许可】

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