Projektbeschreibung
Ermöglichung einer neuen Art von Quantenkomprimierung
Ein neuer Rahmen für die Ausweitung der Gitterfortschritte auf das Kontinuum und die Quantenfeldtheorie ist im Entstehen begriffen. In diesem Kontext wird das ERC-finanzierte Projekt QFT.zip kontinuierliche Tensornetzzustände entwickeln, indem es direkt im Kontinuum arbeitet. Das Projektforschungsteam wird Zustände niedriger Energie der Quantenfeldtheorie auf eine endliche und kleine Anzahl von Parametern komprimieren, was zur numerischen Lösung sehr generischer, stark gekoppelter Theorien in einer vollständig nicht-störungstheoretischen Weise führt. Die Projektarbeit wird beweisen, dass eine derartige Komprimierung möglich ist, was eine erhebliche Verschiebung der derzeitigen Paradigmen in Bezug auf Vielteilchen-Quantenzustände zur Folge haben wird.
Ziel
Many-body quantum systems with strong correlations are particularly difficult to understand in the continuum, where non-perturbative techniques are in scarce supply. Direct diagonalization methods are not available, since the Hilbert space is simply too large to be manageable. This inhibits progress in high energy physics, nuclear physics, and in the study of exotic topological phases of matter. On the lattice, tensor network states, a variational class of wavefunctions coming from quantum information theory, have allowed to compress exponentially large Hilbert spaces down to a smaller numerically manageable corner. This has allowed substantial theoretical and numerical advance on the many-body problem on the lattice.
This project will develop continuous tensor network states, a new framework to extend the recent lattice progress to the continuum and quantum field theory (QFT). The originality of the approach is that it will not rely on any discretization of space-time. I will work directly in the continuum, without any cutoff. Low energy states of quantum field theories, which a priori live in a continuously infinite dimensional Hilbert space, will be compressed down to a finite and small number of parameters. This will then allow to solve numerically very generic (non-integrable) strongly coupled theories in a fully non-perturbative manner. Such a compression was long thought to be impossible, in particular in the relativistic case, but I overcame crucial theoretical hurdles in the past year, making the proposal particularly timely.
I will construct this framework with 3 main applications in mind: i) non-relativistic problems in 2 space dimensions and more, including e.g. fractional quantum Hall states, ii) relativistic QFT, starting with 1+1 dimensional toy model and gradually increasing complexity to get closer to nonabelian gauge theories, iii) critical quantum systems (and classical statistical mechanics).
Wissenschaftliches Gebiet
Not validated
Not validated
- natural sciencesmathematicspure mathematicsalgebralinear algebra
- natural sciencesphysical sciencesnuclear physics
- natural sciencesphysical sciencesquantum physicsquantum field theory
- natural sciencesphysical sciencesclassical mechanicsstatistical mechanics
- natural sciencesphysical sciencestheoretical physics
Programm/Programme
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Thema/Themen
Finanzierungsplan
HORIZON-AG - HORIZON Action Grant Budget-BasedGastgebende Einrichtung
75272 Paris
Frankreich