Study of Entanglement and Quantum Correlations in Spin Lattices using Renormalization Group Method

Abstract

In this thesis we have studied the entanglement and global quantum dis cord for spin-1/2 XY model in all dimensions by using quantum renormaliza tion group (QRG) method both analytically and numerically. The existing idea of one dimensional spin chain is extended to two and three dimensional spin chains by considering the square and cubical lattices respectively. By using the Kaddanoff’s block method the QRG technique implemented in all spatial dimensions. The behavior of entanglement provides the insight that how spin-1/2 particles are correlated with each other on a larger scale which have great implications in quantum information theory. The variation of en tanglement is computed using concurrence as its quantifier. It demonstrates that at what values of the controlling parameters anisotropy γ and coupling strength J of XY model, the large system of spins is how much correlated. In the numerical comparative study of the model it is shown that the con currence has the similar qualitative behavior in all spatial dimensions but quantitatively, its maximum value decreases as the dimensionality of the sys tem increases. Furthermore, global quantum discord (GQD) is also explored along with entanglement for two-dimensional XY model with Dzyaloshinskii Moriya (DM) Interaction which has shown different variations as compared to the entanglement. Apart from this , both concurrence and the GQD cap tures the critical behavior of the spin system and obtained the phenomenon of quantum phase transition in thermodynamic limit which has applications in condense matter theory and also in the development of quantum computers. Further, the system is analyzed using the scaling behavior and entanglement exponent θ is computed which is inverse to the correlation length exponent and provides the information that how the system evolves in the vicinity of the critical point.