We study two different classes of strongly interacting many-body quantum systems in this thesis. The first concerns interacting quantum system with strong disorder. The second is a quantum spin liquid problem. Since many-body quantum systems with strong interaction are difficult in analytic approaches, numerical methods will be used to study these systems.

In the first part of this thesis, we investigate the many-body localization of the 1D spin-1/2 XXZ model with random magnetic field by Exact Diagonalization. We confirm previous results that there exists a mobility edge between ergodic and localized phases at weak disorder. Furthermore, we study the difference between two many-body localization phases in the XXZ model and confirm that there exists a phase transition between t...[ Read more ]

We study two different classes of strongly interacting many-body quantum systems in this thesis. The first concerns interacting quantum system with strong disorder. The second is a quantum spin liquid problem. Since many-body quantum systems with strong interaction are difficult in analytic approaches, numerical methods will be used to study these systems.

In the first part of this thesis, we investigate the many-body localization of the 1D spin-1/2 XXZ model with random magnetic field by Exact Diagonalization. We confirm previous results that there exists a mobility edge between ergodic and localized phases at weak disorder. Furthermore, we study the difference between two many-body localization phases in the XXZ model and confirm that there exists a phase transition between two kinds of many-body localization. Surprisingly, we observe a narrow region of ergodic phase that exists between the two MBL phases. We call the phase Many-Body Ergodic phase since the phase is not analytically connected to the trivial ergodic phase at weak order. In the second part of this thesis, we study the spin -1/2 XXZ spin model on the triangular lattice by mean of Variational Monte Carlo simulation on a class of resonant valence bond (RVB) trial wave-functions. We find that as a function of J_⊥/J_z, there exists a transition point where magnetic order vanishes (at J_⊥/J_z ~ 0.45). Moreover, two kinds of RVB states competed in the Ising regime when J_⊥/J_z < 0.23.