ar X iv : c on d - m at / 9 60 31 56 v 2 2 7 M ar 1 99 6 Modular Invariance , Self - Duality and The Phase Transition Between Quantum Hall Plateaus
نویسنده
چکیده
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting charged particles. One of the models is manifestly invariant under both Duality and Periodic shifts of the statistical angle and, hence, it has a full Modular Invariance. We derive the transformation laws for the correlation functions under the modular group and use them to derive symmetry constraints for the conductances. These allow us to calculate exactly the conductivities at the modular fixed points. We show that, at least at the modular fixed points, the system is critical. Away from the fixed points, the behavior of the model is determined by extra symmetries such as Time Reversal. We speculate that if the natural connection between spin and statistics holds, the model may exhibit an effective analyticity at low energies. In this case, the conductance is completely determined by its behavior under modular transformations. Typeset using REVTEX 1
منابع مشابه
ar X iv : c on d - m at / 9 60 31 56 v 1 2 5 M ar 1 99 6 Modular Invariance , Self - Duality and The Phase Transition Between Quantum Hall Plateaus
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting charged particles. One of the models is manifestly invariant under both Duality and Periodic shifts of the statistical angle and, hence, it has a full Modular Inva...
متن کاملar X iv : c on d - m at / 9 60 62 12 v 2 4 J ul 1 99 6 Quantum Hall Transitions in ( TMTSF )
We have studied the temperature dependence of the integer quantum Hall transitions in the molecular crystal (TMTSF)2PF6. We find that the transition width between the quantum Hall plateaus does not exhibit the universal power-law scaling behavior of the integer quantum Hall effect observed in semiconducting devices. Instead, the slope of the ρxy risers, dρxy/dB, and the (inverse) width of the ρ...
متن کاملar X iv : c on d - m at / 9 60 40 14 v 1 2 A pr 1 99 6 Quantum Hall Effect and Chaotic Motion in Phase Space
We discuss the relation between the Quantum Hall behaviour of charged carriers and their chaotic motion in phase space. It is shown that the quantum Hall diagram is comparable with the stepped diagram in phase space of a chaotic motion.
متن کاملar X iv : c on d - m at / 9 60 31 90 v 1 2 9 M ar 1 99 6 The Four - Dimensional XY Spin Glass
متن کامل
ar X iv : c on d - m at / 9 60 62 12 v 1 2 8 Ju n 19 96 Quantum Hall Transitions in ( TMTSF
We have studied the temperature dependence of the integer quantum Hall transitions in the molecular crystal (TMTSF)2PF6. We find that the transition width between the quantum Hall plateaus does not exhibit the universal power-law scaling behavior of the integer quantum Hall effect observed in semiconducting devices. Instead, the slope of the ρxy risers, dρxy/dB, and the (inverse) width of the ρ...
متن کامل