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The Hall Plateau Transition and non-unitary Quantum Field Theory

The Hall Plateau Transition and non-unitary Quantum Field Theory

Objective

I propose to solve the Quantum Field Theory (QFT) describing the transition between plateaus of quantized Hall conductance in the Integer Quantum Hall Effect (IQHE).
The existence of the plateaus and their topological origin are certainly well understood. In sharp contrast, the transition, which mixes the effects of disorder, magnetic field and possibly interactions, remains very mysterious. Numerical studies of lattice models are plagued by disorder. The QFT description involves physics at very strong coupling, and requires a non-perturbative solution before quantitative predictions can be made.
Finding such a solution is very difficult because the QFT for the plateau transition is ‘non-unitary’ - it involves a non-Hermitian ‘Hamiltonian’. Non-unitary QFT is a challenging, almost unexplored topic, that must be first developed before the plateau transition can be addressed.
I propose to carry out this task with a cross-disciplinary strategy that uses ideas and tools from conformal field theory, statistical mechanics, and mathematics. Key to this strategy is a new and powerful way of analyzing lattice regularizations of the QFTs by focussing on their algebraic properties directly on the lattice, with a mix of advanced representation theory and numerical techniques.
The results - in particular, concerning conformal invariance and renormalization group flows in the non-unitary case - will then be used to solve the QFT models for the plateau transition in the IQHE and in other universality classes of 2D Anderson insulators. This will be a landmark step in our understanding of the localization/delocalization transition in two dimensions, and allow a long delayed comparison of theory with experiment. The results will, more generally, impact many other areas of physics where non-unitary QFT plays a central role - from disordered systems of statistical mechanics to the string theory side of the AdS/CFT duality, to the effective description of open quantum systems.
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Host institution

COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES

Address

Rue Leblanc 25
75015 Paris 15

France

Activity type

Research Organisations

EU Contribution

€ 2 098 157,50

Beneficiaries (1)

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COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES

France

EU Contribution

€ 2 098 157,50

Project information

Grant agreement ID: 669205

Status

Ongoing project

  • Start date

    1 October 2015

  • End date

    30 September 2020

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 2 098 157,50

  • EU contribution

    € 2 098 157,50

Hosted by:

COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES

France