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The Hall Plateau Transition and non-unitary Quantum Field Theory

Project description

Research investigates electrical conductance transitions in 2D electron systems

The quantum Hall effect is observed in 2D electron systems subjected to low temperatures and strong magnetic fields, in which electrical conductance changes in discrete steps called plateaus. The ERC-funded NuQFT project aims to solve the quantum field theory (QFT), a theoretical framework used to describe these transitions between plateaus of quantised Hall conductance. Although the existence and topological origin of the plateaus are well understood, the transition remains mysterious owing to the non-unitary nature of the QFT. Combining conformal field theory, statistical mechanics and mathematics, researchers will analyse lattice regularisations of QFTs by examining their algebraic properties directly on the lattice. Project results could enhance understanding of the localisation/delocalisation transition in two dimensions and generally impact disordered systems, string theory, and open quantum systems.

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.

Host institution

COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
Net EU contribution
€ 2 098 157,50
Address
RUE LEBLANC 25
75015 PARIS 15
France

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Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
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Total cost
€ 2 098 157,50

Beneficiaries (1)