Project description DEENESFRITPL Making possible a new type of quantum compression A new framework to extend lattice progress to the continuum and quantum field theory is in the making. To that end, the ERC-funded QFT.zip project will develop continuous tensor network states by working directly in the continuum. Project researchers will compress low energy states of quantum field theory down to a finite and small number of parameters, leading to the solution of numerically very generic strongly coupled theories in a fully non-perturbative manner. Project work will prove that compression of this kind is possible, significantly shifting current paradigms on many-body quantum states. Show the project objective Hide the project objective Objective 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). Fields of science natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesphysical sciencesnuclear physicsnatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesphysical sciencesclassical mechanicsstatistical mechanicsnatural sciencesphysical sciencestheoretical physics Programme(s) HORIZON.1.1 - European Research Council (ERC) Main Programme Topic(s) ERC-2021-STG - ERC STARTING GRANTS Call for proposal ERC-2021-STG See other projects for this call Funding Scheme HORIZON-AG - HORIZON Action Grant Budget-Based Coordinator ASSOCIATION POUR LA RECHERCHE ET LE DEVELOPPEMENT DES METHODES ET PROCESSUS INDUSTRIELS Net EU contribution € 938 705,00 Address Boulevard saint michel 60 75272 Paris France See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Participants (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all Third-party Legal entity other than a subcontractor which is affiliated or legally linked to a participant. The entity carries out work under the conditions laid down in the Grant Agreement, supplies goods or provides services for the action, but did not sign the Grant Agreement. A third party abides by the rules applicable to its related participant under the Grant Agreement with regard to eligibility of costs and control of expenditure. ECOLE NATIONALE SUPERIEURE DES MINES DE PARIS France Net EU contribution € 288 750,00 Address Boulevard saint michel 60 75272 Paris See on map Region Ile-de-France Ile-de-France Paris Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Partners (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE France Net EU contribution € 0,00 Address Domaine de voluceau rocquencourt 78153 Le chesnay cedex See on map Region Ile-de-France Ile-de-France Yvelines Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
