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Magnetisation, Phases & Phase Transitions in Frustrated and Unfrustrated XY Model

Electronic Theses of Indian Institute of Science

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Title Magnetisation, Phases & Phase Transitions in Frustrated and Unfrustrated XY Model
 
Creator Maji, Maheswar
 
Subject Phase Transformations
Magnetisation
High Tc Superconductors
XY Model
Condensed Matter Physics - Models
XY Models - Magnetisation
XY Models - Phase Transitions
Bose-Hubbard Model
2D and 3D XY Models
Chiral Mott Insulator
Condensed Matter Physics
 
Description Through our whole work we study the XY model with all its entirety, a particular spin model where spins are confined in a plane. We try to bring out a good understanding of this model with all different types of phases and phase transition, it undergoes in critical situations. We conceive of these external conditions from very different physical models like High Tc Superconductor, Ultracold atoms in optical lattice which are in focus of recent research. Firstly we model high Tc Superconductors with very simple 2D XY model to get an idea about the diamagnetic response exhibited by these materials when kept in a external magnetic field. This modeling is reasonable because most of the physics of cuprate High Tc Superconductors are governed by their 2D copper oxide planes which insists us to consider 2D models. Later we shifted to a more realistic 3D anisotropic XY model , as the coupling between cuprates plane may have a considerable role in devising physics of those materials. We particularly focus on the 2D to 3D crossover effect on magnetisation showed by these models, with keeping an eye on how all these can be relate to the experimentally acquired magnetisation profile of High Tc Supercondutors. On the second project we investigate on the phase diagram of a fully frustrated 2-leg ladder Bose Hubbard model. After mapping it properly to a classical model, a bi-layer Fully Frustrated XY model on square lattice, we found that the frustration leads to the emergence of a new phase "Chiral Mott insulator(CMI)" sandwiched between "Chiral Superfluid(CSF)" and "regular Mott insulator(MI)" phase.
We divide the whole report into four parts. The first chapter is basically contain-ing introductory part comprising the motivation. In the second chapter we discuss various types of phases and phase transitions of the 2D & 3D XY models. We try to address their critical behaviors. In the third chapter and onwards we consider our model in external magnetic field and observe magnetisation in these systems. Here we specially focus on 2D to 3D crossover effect on magtisation measurement. Lastly in the fourth chapter we bring out a correspondence of XY model with the 2 leg ladder fully frustrated Bose Hubbard Model. There we report the emergence of a new phase, Chiral Mott Insulator(CMI) due to frustration in system.
 
Contributor Mukerjee, Subroto
 
Date 2018-02-22T20:27:24Z
2018-02-22T20:27:24Z
2018-02-23
2011
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/3168
http://etd.ncsi.iisc.ernet.in/abstracts/4028/G25554-Abs.pdf
 
Language en_US
 
Relation G25554