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The Hall Plateau Transition and non-unitary Quantum Field Theory

Total Cost €


EC-Contrib. €






Project "NuQFT" data sheet

The following table provides information about the project.


Organization address
address: RUE LEBLANC 25
city: PARIS 15
postcode: 75015

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Project website
 Total cost 2˙098˙157 €
 EC max contribution 2˙098˙157 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2015
 Duration (year-month-day) from 2015-10-01   to  2021-06-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project 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.


year authors and title journal last update
List of publications.
2017 R. Vasseur, A. Roshani, S. Haas, H. Saleur
Healing of defects in random antiferromagnetic spin chains
published pages: 50004, ISSN: 0295-5075, DOI: 10.1209/0295-5075/119/50004
EPL (Europhysics Letters) 119/5 2020-01-21
2016 Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur
The continuum limit of a N − 1 ( 2 ) spin chains
published pages: 52-93, ISSN: 0550-3213, DOI: 10.1016/j.nuclphysb.2016.07.026
Nuclear Physics B 911 2020-01-21
2017 Lorenzo Campos Venuti, Zhengzhi Ma, Hubert Saleur, Stephan Haas
Topological protection of coherence in a dissipative environment
published pages: , ISSN: 2469-9926, DOI: 10.1103/physreva.96.053858
Physical Review A 96/5 2020-01-21
2017 Romain Couvreur, Jesper Lykke Jacobsen, Hubert Saleur
Entanglement in Nonunitary Quantum Critical Spin Chains
published pages: , ISSN: 0031-9007, DOI: 10.1103/physrevlett.119.040601
Physical Review Letters 119/4 2020-01-21
2018 Jonathan Belletête, David Ridout, Yvan Saint-Aubin
Restriction and induction of indecomposable modules over the Temperley–Lieb algebras
published pages: 45201, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aa993a
Journal of Physics A: Mathematical and Theoretical 51/4 2020-01-21
2018 Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur
A distribution approach to finite-size corrections in Bethe Ansatz solvable models
published pages: 96-117, ISSN: 0550-3213, DOI: 10.1016/j.nuclphysb.2018.06.001
Nuclear Physics B 934 2020-01-21

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