Entanglement and bell correlations in strongly correlated many-body quantum systems
- Autores: Angelo Piga
- Directores de la Tesis: Maciej Lewenstein (dir. tes.), Shi Ju Ran (codir. tes.)
- Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2020
- Idioma: español
- Materias:
- Texto completo no disponible (Saber más ...)
- Resumen
During the past two decades,thanks to the mutual fertilization of the research in quantum information and condensed matter, new approaches based on purely quantum features without any classical analog turned out to be very useful in thecharacterizationofmany-bodyquantumsystems(MBQS).Apeculiarroleis obviously played by the study of purely quantum correlations, manifesting in the “spooky” properties of entanglement and nonlocality (or Bell correlations), which ultimately discriminate classical from quantum regimes. It is, in fact, such kind of correlations that give rise to the plethora of intriguing emergent behaviorsofMBQS,whichcannotbereducedtoameresumofthebehaviorsof individual components, the most important example being the quantum phase transitions. However, despite being indeed closely related concepts, entanglement and nonlocality are actually two different resources. With regard to the entanglement, we will use it to characterize several instances of MBQS, to exactly locate and characterize quantum phase transitions in spin-lattices and interacting fermionic systems, to classify different gapped quantum phases according to their topological features and to provide a purely quantum signature of chaos in dynamical systems. Ourapproachwillbemainlynumericalandforsimulatingthegroundstates of several one-dimensional lattice systems we draw heavily on the celebrated “densitymatrixrenormalizationgroup”(DMRG)algorithminthe“matrixproduct state” (MPS) ansatz. A MPS is a one-dimensional tensor network (TN) representation for quantum states and occupies a pivotal position in what we have gained in thinking MBQS from an entanglement perspective. In fact, the success of TNs states mainly relies on their ful¿llment, by construction, of the socalled “entanglement area law”. This is a feature shared by the ground states of gapped Hamiltonians with short-range interactions among the components and consists of a sub-extensive entanglement entropy, which grows only with the surface of the bipartition. This property translates in a reduced complexity ofsuchsystems,allowingaffordablesimulations,withanexponentialreduction ofcomputationalcosts. BesidestheuseofalreadyexistingTN-basedalgorithms, an effort will be done to develop a new one suitable for high-dimensional lattices. Whilemanyusefulresultsareavailablefortheentanglementinmanydifferent contexts, less is known about the role of nonlocality. Formally, a state of a multi-party system is de¿ned nonlocal if its correlations violate some “Bell inequality” (BI). The derivation of the BIs for systems consisting of many parties is a formidable task and only recently a class of them, relevant for nontrivial states, has been proposed. In an important chapter of the thesis, we apply these BIstofullycharacterizethephasetransitionofalong-rangeferromagneticIsing model, doing a comparison with entanglement-based results and then making one of the ¿rst efforts in the study of MBQS from a nonlocality perspective
