Quantum Phases and Magnetization Plateaus of Skewed Spin Ladders

Abstract

This thesis deals with theoretical studies of skewed spin ladders which are two legged ladder with periodic slanted rung bonds and can be viewed as periodic fused rings with two different number of vertices. The spin at the vertices (sites) considered in this thesis are either spin ½ or 1. The skewed ladder is named an n/m ladder when the fused adjacent rings are with n and m vertices. These are quasi one-dimensional systems. The systems are studied by varying the rung exchange $J_1$, keeping the nearest neighbor leg exchange $J_2$ fixed at unity. The first chapter gives a brief historical introduction and discusses the origin of exchange interactions in materials. The spin-1/2 and spin-1 chains and quantum phases of the frustrated and dimerized spin-1/2 chains as well as the qualitative distinction between spin-1/2 and spin-1 antiferromagnetic Heisenberg chains are discussed. For investigating the skewed ladder systems, computational methods such as exact diagonalization technique in valence bond (VB) and constant Ms basis is described in chapter 2. For studying the large systems closer to the thermodynamic limit, the density matrix renormalization group (DMRG) method is introduced. Both finite and infinite DMRG algorithms are discussed and their implementation are outlined. Chapter three presents the quantum phases in a 5/7 spin-1 skewed ladder system, studied numerically using the exact diagonalization technique up to 16 spins and the density matrix renormalization group method for larger system sizes. The study of diverse gs properties such as spin gap, spin-spin correlations, spin density, and bond order reveals that the system has four distinct phases, namely, the AF phase at small $J_1$; the ferrimagnetic phase with gs spin $S_G = n$ for $1.44 lt J_1 lt 4.74$ and with $S_G = 2n$ for $J_1 gt 5.63$, where n is the number of unit cells; and a reentrant nonmagnetic phase at $4.74 lt J_1 lt 5.44$. The system also shows the presence of spin current at specific $J_1$ values due to simultaneous breaking of both refl...