Objetivo 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. Ámbito científico natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencescomputer and information sciencesartificial intelligencemachine learningnatural sciencesphysical scienceselectromagnetism and electronicssuperconductivity Palabras clave Spectrum of quantum Hamiltonians classification of quantum phases locally interacting quantum spin systems dissipation in quantum systems computability tensor networks Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-CoG-2014 - ERC Consolidator Grant Convocatoria de propuestas ERC-2014-CoG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-COG - Consolidator Grant Institución de acogida UNIVERSIDAD COMPLUTENSE DE MADRID Aportación neta de la UEn € 1 462 750,00 Dirección AVENIDA DE SENECA 2 28040 Madrid España Ver en el mapa Región Comunidad de Madrid Comunidad de Madrid Madrid Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 462 750,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo UNIVERSIDAD COMPLUTENSE DE MADRID España Aportación neta de la UEn € 1 462 750,00 Dirección AVENIDA DE SENECA 2 28040 Madrid Ver en el mapa Región Comunidad de Madrid Comunidad de Madrid Madrid Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 462 750,00