Supervisor: Arianna Montorsi
The proposed research project focuses on the study of strongly correlated quantum matter, especially in low dimensions where the laws of quantum mechanics and the role of entanglement emerge the most, even at the macroscopic scale. These systems exhibit peculiarities such as the breakdown of the Landau theory of phase transitions, leading to the emergence of a variety of exotic low-temperature phases with non-local trivial and non-trivial topological orders. These phases include the Haldane phase of integer spin systems, symmetry-protected topological superconductors and insulators, and more generally low-temperature deconfined quantum phases, where some degrees of freedom can order in the disordered background of others without breaking any of the Hamiltonian symmetries. The reference Hamiltonian for studying correlated quantum matter is the Hubbard model, which can be analyzed using a range of analytical and numerical approaches for both bosons and fermions. Experimental investigation of these systems can be carried out through quantum simulation using appropriate ultracold quantum gases of atoms and molecules.
In this project, we provide a systematic approach to studying quantum deconfined phases of Hubbard-like systems through the use of disorder operators. We will exploit both bosonization and renormalization group analytical techniques, as well as density matrix renormalization group, matrix product states, and quantum Monte Carlo numerical approaches. Through the investigation of the role of nonlocal orders in the emergence and stability of both topological trivial and non trivial phases in these systems, the project ultimately aims at the discovery of new mechanisms underlying superconducting and insulating properties of quantum matter.
- PE3_6 Macroscopic quantum phenomena, e.g. superconductivity, superfluidity, quantum Hall effect
- PE3_8 Magnetism and strongly correlated systems
- PE3_15 Statistical physics: phase transitions, condensed matter systems, models of complex systems, interdisciplinary applications
- PE2_11 Ultra-cold atoms and molecules