THESIS
2020
xiii, 79 pages : illustrations (some color) ; 30 cm
Abstract
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...[
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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.
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