PhD Dissertation Defense: Barış Çakmak

QUANTUM CORRELATIONS IN SPIN CHAINS AND HIGHLY SYMMETRIC

STATES

Barış Çakmak
Physics, PhD Dissertation, 2014

Thesis Jury

Assoc. Prof. Zafer Gedik (Thesis Advisor), Prof. Dr. Cihan Saçlıoğlu, Assoc. Prof. Dr. İsmet İnönü Kaya, Assoc. Prof. Dr. Özgür Erçetin, Prof. Dr. Özgür Esat Müstecaplıoğlu

Date & Time: July 10th, 2014 –  1.40 PM

Place: FENS L-035

Abstract

Non-classical correlations arise in various quantum mechanical systems. Characterization and quantification of these correlations is an important branch in the field of quantum information theory and still a subject of active research. Moreover, investigating non-classical correlations in condensed matter systems gives important insights about these systems. Especially, systems possessing a quantum critical point in their phase diagrams have attracted much attention due to peculiar behavior of correlations near these points. In this thesis, we have explored two distinct quantum spin models from correlations perspective. On the other hand, we discuss the correlation content of an important subclass of bipartite states. We start by analytically calculating the quantum discord for a system composed of spin-j and spin-1/2 subsystems possessing rotationally symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in our case amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have also compared their quantum discord with entanglement. Next, we investigate the thermal quantum and total correlations in the anisotropic XY spin-chain with transverse magnetic field. We show that the ability of the measures to estimate the critical points of the system at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. Furthermore, we study the effect of temperature on long-range correlations of the system. Finally, we study the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. We demonstrate that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement.