The integer quantum Hall plateau transition is a current algebra after all

Abstract

The scaling behavior near the transition between plateaus of the Integer Quantum Hall Effect (IQHE) has traditionally been interpreted on the basis of a two-parameter renormalization group (RG) flow conjectured from Pruisken's non-linear sigma model (NLσM). Yet, the conformal field theory (CFT) describing the critical point remained elusive, and only fragments of a quantitative analytical understanding existed up to now. In the present paper we carry out a detailed analysis of the current-current correlation function for the conductivity tensor, initially in the Chalker-Coddington network model for the IQHE plateau transition and then in its exact reformulation as a supersymmetric vertex model. We develop a heuristic argument for the continuum limit of the non-local conductivity response function at criticality and thus identify a non-Abelian current algebra at level n = 4. Based on precise lattice expressions for the CFT primary fields we predict the multifractal scaling exponents of critical wavefunctions to be ∆ q = q(1 − q)/4. The Lagrangian of the RG-fixed point theory for r retarded and r advanced replicas is proposed to be the GL(r|r) n=4 Wess-Zumino-Witten model deformed by a truly marginal perturbation. The latter emerges from the NLσM by a natural scenario of spontaneous symmetry breaking.

Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator

“…Recently, the high-precision numerical calculations show that the correlation length exponent ν of the Chalker-Coddington model is~2.6 [22][23][24] instead of~2.33. It is noteworthy that the larger νvalue is also supported by the recent field theory analysis 25 . As a consequence, the critical exponent κ = p/2ν ∼ 0.38, if we assume p = 2 is in good agreement with the κ-value obtained in our experiment.…”

“… . The exponent κ is found to be 0.38 ± 0.02, smaller than the previously believed value κ ∼ 0.43 for the QH plateau-to-plateau transition 4 , 20 , 21 , but in good agreement with the recent high-precision numerical results on the Chalker–Coddington network model, which yields a correlation length exponent ν ~ 2.6 if the dynamic exponent p = 2 22 – 25 . The experimental results are supported by theoretical arguments that the QAH to axion insulator phase transition, just like the QH plateau-to-plateau transition, can also be described using the Chalker–Coddington network model.…”

On truncations of the Chalker-Coddington model

“…Finally, we note that while this paper was being completed, a new proposal appeared for the CFT of the Chalker-Coddington model, which involves, in particular, a level-four GL(1|1) Wess-Zumino-Witten model [43]. More work is needed to see whether our results are more compatible with this proposal than with previous ones.…”

“…More work is needed to see whether our results are more compatible with this proposal than with previous ones. Note that in [43], the value for ν is expected to be ν = ∞, despite the large but certainly finite values obtained in simulations on the CC model. with…”

Poisson-Lie T-duality of WZW model via current algebra deformation

“…In the context of two-dimensional conformal field theories, gauged WZW models with coset target spaces are investigated since many years (see [59,60] for early contributions). Recently, nonlinear sigma models found new applications in statistical mechanics, describing certain twodimensional systems at criticality [61], as well as in condensed matter physics, describing transitions for the integer quantum Hall effect [62].…”