Objectif Interactions in a many body quantum system are encoded in a Hamiltonian, where the physical intuition that particles can only interact with those which are closeby is formally imposed as a local structure in the Hamiltonian, and homogeneity in space is imposed by a translational invariant structure on a given regular lattice in one, two or three dimensions. The first main aim of this proposal is to characterize the existence of a uniform (with the system size) lower bound on the gap between the two lowest eigenvalues of a given local translational invariant Hamiltonian.There are many reasons which motivate this study, coming from different fields, and hence many potential applications. We will concentrate here on those coming from quantum information theory and from condensed matter physics and mainly, as the second main aim of this proposal, on classifying the different possible quantum phases arising in this type of models. Champ scientifique natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencescomputer and information sciencesartificial intelligencemachine learningnatural sciencesphysical scienceselectromagnetism and electronicssuperconductivity Mots‑clés Spectrum of quantum Hamiltonians classification of quantum phases locally interacting quantum spin systems dissipation in quantum systems computability tensor networks Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-CoG-2014 - ERC Consolidator Grant Appel à propositions ERC-2014-CoG Voir d’autres projets de cet appel Régime de financement ERC-COG - Consolidator Grant Institution d’accueil UNIVERSIDAD COMPLUTENSE DE MADRID Contribution nette de l'UE € 1 462 750,00 Adresse AVENIDA DE SENECA 2 28040 Madrid Espagne Voir sur la carte Région Comunidad de Madrid Comunidad de Madrid Madrid Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 462 750,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire UNIVERSIDAD COMPLUTENSE DE MADRID Espagne Contribution nette de l'UE € 1 462 750,00 Adresse AVENIDA DE SENECA 2 28040 Madrid Voir sur la carte Région Comunidad de Madrid Comunidad de Madrid Madrid Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 462 750,00