Abstract
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker–Coddington network model and a supersymmetric vertex model.
Highlights
Among the critical phenomena in two-dimensional quantum systems with disorder, the transition between Hall conductance plateaus of the integer quantum Hall effect stands out as a possible paradigm for quantumphase transitions of Anderson-localization type
In spite of numerous efforts [1, 2, 3] and a renewed interest coming from the expanding research area of symmetry-protected topological phases [4], the IQHE transition has so far defied an analytical solution by the methods of conformal field theory and/or the theory of integrable systems
From a Lagrangian perspective, what we are after is the conformal field theory of a single scalar field φ such that Vq(z, z) = eqφ(z,z). (Such a field φ exists due to Vq ∼ (B+C−)q and the positivity of B+C− .) The Lagrangian should emerge from the full theory as an effective Lagrangian by integrating out all the other fields
Summary
Among the critical phenomena in two-dimensional quantum systems with disorder, the transition between Hall conductance plateaus of the integer quantum Hall effect (referred to as the IQHE transition for short) stands out as a possible paradigm for quantumphase transitions of Anderson-localization type. An important technical point is that the Lie algebra of the non-compact sector has more than one conjugacy class of Cartan subalgebras, and one must choose the correct class to obtain highest-weight vectors that are positive and give rise to a continuum of scaling fields. To implement these highest-weight ideas, we derive new identities for a generating function relating wavefunction observables of the network model to correlation functions of the vertex model.
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