Superuniversality of dimerized SU(N plus M) spin chains

Article

关键词: (MIS-)HANDLING GAUGE-INVARIANCE;    QUANTUM HALL TRANSITION;    NONLINEAR SIGMA-MODELS;    LARGE-N LIMIT;    SUPER UNIVERSALITY;    INSTANTON VACUUM;    RENORMALIZATION;    FIELD;   

DOI  :  10.1103/PhysRevB.105.155111

来源: SCIE

【 摘 要 】

We explore the physics of the quantum Hall effect using the Haldane mapping of dimerized SU(N + M) spin chains, the large N expansion, and the density matrix renormalization group technique. We show that while the transition is first order for N + M > 2, the system at zero temperature nevertheless displays a continuously diverging length scale xi (correlation length). The numerical results for (N, M) = (3, 1), (2, 2), ( 5, 1), and (7, 1) indicate that xi is a directly observable physical quantity, namely the spatial width of the edge states. We relate the physical observables of the quantum spin chain to those of the quantum Hall system (and, hence, the upsilon vacuum concept in quantum field theory). Our numerical investigations provide strong evidence for the conjecture of superuniversality which says that the dimerized spin chain quite generally displays all the basic features of the quantum Hall effect, independent of the specific values of N and M. For the cases at hand we show that the singularity structure of the quantum Hall plateau transitions involves a universal function with two scale parameters that may in general depend on N and M. This includes not only the Hall conductance but also the ground state energy as well as the correlation length xi with varying values of upsilon similar to pi.

【 授权许可】

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