Emergent Phenomena and Transport in Correlated Low Dimensional Quantum Systems A Global Coordinate perspective

Mukherjee, Anirban (2014) Emergent Phenomena and Transport in Correlated Low Dimensional Quantum Systems A Global Coordinate perspective. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

In this thesis we study three di�erent many body problem's belonging to di�erent dimensionality. The Kondo Problem involves a single point like impurity in a metal therefore this problem is 0D. The XXZ Problem involves spins placed on a 1D lattice. The Quantum Hall Problem involves a 2D electron gas placed in a strong magnetic �eld. Furthermore this three problem involves di�erent types of interactions, single body potentials, etc. The Kondo Problem involves interaction of local conduction electron spin density with the impurity spin and exchange of spin angular momentum between the bath of conduction electrons and the impurity spin. The XXZ problem corresponds to spins interacting with its nearest neighboring spins on a 1D lattice via spin ipping mechanism and ising interaction. The Quantum Hall problem involves electrons on a two dimensional space interacting via electron-electron potential, here magnetic �eld is a single body potential. Another interesting di�erence is two of the problems that is the Kondo Problem and the Quantum Hall problem happen in continuous space. Whereas the XXZ problem happens on a 1D lattice. Devoid of all this di�erences among the three problems as we show in this thesis all these three problems are connected.

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