THESIS
2018
xiii, 104 pages : illustrations ; 30 cm
Abstract
Correlated many body systems remain at the center of research in condensed matter theory for their
rich properties and possible phase transitions. In the recent years, trapped atomic gases provide a
unique playground to simulate many-body quantum physics in a very controlled way. The theoretical
study on the properties of these cold atom systems thus become important. In this thesis, we
address the theoretical studies on two cold atom models: an impurity model and a bosonic model
with k-space Berry curvature. Explicitly, we first study in Chap.2 an impurity model interacting
with a large bath of cold atoms. This model is mapped into a spin-boson model using either the
Bogoliubov theory (for bosonic atoms) or bosonization (for fermionic atoms) and the corresponding
dissipative ph...[
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Correlated many body systems remain at the center of research in condensed matter theory for their
rich properties and possible phase transitions. In the recent years, trapped atomic gases provide a
unique playground to simulate many-body quantum physics in a very controlled way. The theoretical
study on the properties of these cold atom systems thus become important. In this thesis, we
address the theoretical studies on two cold atom models: an impurity model and a bosonic model
with k-space Berry curvature. Explicitly, we first study in Chap.2 an impurity model interacting
with a large bath of cold atoms. This model is mapped into a spin-boson model using either the
Bogoliubov theory (for bosonic atoms) or bosonization (for fermionic atoms) and the corresponding
dissipative phase transitions are found, consistent with previous theories. In Chap.3, we study
the properties of cold bosons in a two-dimensional optical lattice system where Bose-Einstein-condensation
occurs at a momentum point k with non-zero k-space Berry curvature. We show
that the boson system carries non-universal equilibrium angular momentum and edge current at
low temperatures. On the other hand, exact solutions of some special quantum interacting particle
models are important resources for understanding the physics of strongly correlated systems. In
Chap.4, we generalize a solvable Falicov-Kimball model[3] in two general classes: spin-dependent
hopping class and the Majorana Falicov-Kimball class. We explore the general criteria for exact
solubilities in these two classes for arbitrary interaction strength. Corresponding to the two classes,
we explicitly study two models: (1) a spin-dependent Haldane Hubbard model, in which we found
an interaction-driven topological phase transition; and (2) a p-wave BCS Hubbard model in a bipartite
lattice, in which we found chargeless solitonic excitation and interaction dependent spin
excitation.
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