European Commission logo
français français
CORDIS - Résultats de la recherche de l’UE
CORDIS

Compressing many-body quantum states in continuous space-time with tensor networks

Description du projet

Rendre possible un nouveau type de compression quantique

Un nouveau cadre permettant d’étendre les progrès du réseau au continuum et à la théorie quantique des champs est en cours d’élaboration. À cette fin, le projet QFT.zip financé par le CER, développera des états de réseaux tensoriels continus en travaillant directement dans le continuum. Les chercheurs du projet comprimeront les états de basse énergie de la théorie quantique des champs jusqu’à un nombre fini et réduit de paramètres, ce qui conduira à la résolution numérique de théories fortement couplées très génériques d’une manière totalement non-perturbative. Les travaux du projet démontreront la possibilité d’une telle compression, ce qui modifiera considérablement les paradigmes actuels sur les états quantiques à corps multiples.

Objectif

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).

Institution d’accueil

ASSOCIATION POUR LA RECHERCHE ET LE DEVELOPPEMENT DES METHODES ET PROCESSUS INDUSTRIELS
Contribution nette de l'UE
€ 938 705,00
Adresse
BOULEVARD SAINT MICHEL 60
75272 Paris
France

Voir sur la carte

Région
Ile-de-France Ile-de-France Paris
Type d’activité
Research Organisations
Liens
Coût total
€ 1 227 455,00

Bénéficiaires (2)

Partenaires (1)