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

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).

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

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Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
Other funding
€ 0,00

Participants (1)

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

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Region
Ile-de-France Ile-de-France Paris
Activity type
Higher or Secondary Education Establishments
Other funding
€ 0,00

Partners (1)

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
France
Net EU contribution
€ 0,00
Address
Domaine De Voluceau Rocquencourt
78153 Le Chesnay Cedex

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Region
Ile-de-France Ile-de-France Yvelines
Activity type
Research Organisations
Other funding
No data