Rotating two leg Bose Hubbard ladder
Author
Keleş, Ahmet
Advisor
Oktel, Mehmet Özgür
Date
2009Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
We analyze two leg Bose Hubbard model under uniform magnetic field within various
methods. Before studying the model, we discuss the background on rotating
Bose Einstein condensates, Bose Hubbard model and superfluid Mott insulator
transition. We give a general overview of Density Matrix Renormalization Group
(DMRG) theory and show some of the applications. Introducing two leg system
Hamiltonian, we solve the single particle problem and find distinct structures
above and belove a critical magnetic field αc = 0.21π. Above this value of the
field, it is found that system has travelling wave solutions. To see the effects
of interactions, we use Gross Pitaevskii approximation. Spectrum of the system
below the critical field and the change of αc with the interaction strength are obtained
for small interactions, i.e Un/t < 1. To specify Mott insulator boundary,
variational mean field theory and strong coupling perturbation (SCP) theories
are used. The travelling wave solutions found in single particle spectrum above
αc is found to be persistent in mean field description. On the other hand, comparing
with the strong coupling expansion results, it has been found that the
mean field theory gives poor results, because of the one dimensional structure
of the system. The change of the tip of the lobe where BKT transition takes
place is found as a function of magnetic field by SCP. Finally we use DMRG to
obtain the exact shape of the phase diagram. It is found that second order strong
coupling perturbation theory gives very good results. System is found to display
reenterant phase to Mott insulator. Looking at the infinite onsite interaction
limit via DMRG, the critical value of the magnetic field is found to be exactly
equal to the single particle solution. We have calculated the particle-hole gap for
various fillings and different magnetic fields and found Fractional Quantum Hall
like behaviors.
Keywords
Bose-Hubbard ModelStrongly Correlated Systems
Renormalization
Superfluid-Mott Insulator Transition