Descrizione del progetto
Rendere possibile un nuovo tipo di compressione quantistica
Si sta delineando un nuovo quadro per estendere il progresso reticolare al continuum e alla teoria quantistica dei campi. A tal fine, il progetto QFT.zip finanziato dal CER, svilupperà stati di rete tensoriale continui lavorando direttamente nel continuum. I ricercatori del progetto comprimeranno gli stati a bassa energia della teoria quantistica dei campi fino a un numero finito e ridotto di parametri, portando alla soluzione di teorie fortemente accoppiate numericamente molto generiche, in modo completamente non perturbativo. Il lavoro del progetto dimostrerà che una compressione di questo tipo è possibile, spostando considerevolmente gli attuali paradigmi sugli stati quantistici a molti corpi.
Obiettivo
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).
Campo scientifico
- natural sciencesmathematicspure mathematicsalgebralinear algebra
- natural sciencesphysical sciencesnuclear physics
- natural sciencesphysical sciencesquantum physicsquantum field theory
- natural sciencesphysical sciencesclassical mechanicsstatistical mechanics
- natural sciencesphysical sciencestheoretical physics
Programma(i)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Argomento(i)
Meccanismo di finanziamento
HORIZON-AG - HORIZON Action Grant Budget-BasedIstituzione ospitante
75272 Paris
Francia