The study of the properties of quantum many-body systems is inherently a hard task. In fact, for some cases this is a hard task even for classical systems, but quantum phenomena turn this study an even more difficult problem. The resources needed to study the states populating the Hilbert space of a quantum system grow exponentially with the number of particles. Analytical studies are generally rare, only valid for very specific cases, and numerical alternatives are only practical for a small amount of particles.

Quantum Information Theory provides a novel approach to study and explain fundamental concepts of the quantum theory. In addition, it takes profit of these quantum effects to design new techniques for information processing and manipulation. Current development of Quantum Information Theory has a close connection with the experimental capabilities of light and matter manipulation. Despite its youth, these theoretical and experimental advances have already provided commercial applications.

The thesis is placed in the crossroad of these disciplines, currently a fertile research field. We study local hamiltonians from a quantum information perspective, with implications in Condensed Matter Physics. We focus mainly on numerical methods for the study of many-body systems, showing how known Quantum Information Theory results are useful for the study of complex systems. Our work is mainly numerical, and theoretical results are limited to specific situations. However, we show that common properties emerge in fermionic and bosonic systems as a result of fundamental properties of quantum systems.

We have explored the physical properties of thermal states of many-body systems, corresponding to quantum states of systems affected by thermal noise. Thermal states are present typically in experimental conditions, but their study in the language of Quantum Information Theory proves to be difficult, mainly due to the characterization of mixed-state entanglement. We have presented a constructive way to prove the presence of bound entanglement in thermal states. In addition, we have shown how the local temperature has to be carefully defined inside a quantum system. We conclude that the non-classical behavior of the temperature inside a system appears along with the presence of entanglement.

At low temperatures, the physics of quantum many-body systems is dominated by the properties of the ground state. In 1D far from criticality, local hamiltonians have ground states with an efficient classical representation. We show in the thesis how the interaction range may play a minor role in this picture, which could provide an efficient DMRG simulation of highly connected systems far from the typical scenario of nearest-neighbor interaction. A key property of local hamiltonians relates the entropy between regions with their connecting boundary. These relations, known as area laws, are a fundamental element to the results shown here. Area laws are a paradigm of the relation between Quantum Information Theory concepts, physical systems and geometric considerations. Our results obtained for two completely different families of hamiltonians evidence a fundamental behavior between these systems. These common properties appear due to fundamental considerations, independently on the specific details of the system under study.


Friday, May 14, 11:00. ICFO's Auditorium

Thesis Advisor: Prof. Antonio Acín