My Ph.D. is devoted to the analysis of some exotic quantum phase transitions arising in strongly correlated systems described by spin Hamiltonians.
On the one hand, my studies have focused on quantum phase transitions occurring close to multicritical points. These points are particularly pathological since several quantum phases coexist in a narrow range of Hamiltonian parameters. This fact, as I will discuss in this thesis, has strong effects on the properties displayed by the strongly correlated system. On the other hand, I have also analyzed quantum phase transitions leading to quantum spin liquids which are novel phases of matter occurring in some frustrated systems. These phases are at the forefront of condensed matter research since their characterization remains very elusive both experimentally and theoretically.
The research presented here can be split into three different parts. The first part deals with the unusual behavior of bipartite entanglement in some quantum spin chains. The role of quantum fluctuations is enhanced in low dimensions, and thus 1D systems offer a plethora of possibilities to analyze the role of quantum fluctuations in quantum phase transitions. Some studies have been carried out for spin-1/2 models, while others have been realized for spin-1 systems.
The second part of my thesis covers disordered frustrated quantum systems and, in particular, the presence of quantum spin liquids. Frustration reflects the impossibility of fulfilling simultaneously all constraints posed by some Hamiltonians. It is an inherent property of some strongly correlated systems, e.g., classical spin ice models or 2D quantum antiferromagnets. Such incompatibility often translates into a severe problem of energy minimization when finding the ground state of the system. Many frustrated systems order at zero or low temperatures but there also states that do not order and lay beyond the Landau theory of phase transitions presenting a fascinating underlying structure. Quantum spin liquids belong to this last type. My approach to address their study has been to develop a new numerical method using engineered boundary conditions. Such approach has allowed me to obtain some unambiguous signatures about the nature of some quantum spin liquids.
The last part of my thesis is devoted to describe and analyze frustrated quantum spin models by means of modified spin wave theory. The use of such analytical tool has allowed me to asses the performance and validity of the numerical approach I have developed as well as to deepen my understanding of quantum spin liquids.