From quantum spin chains to square lattice Heisenberg anti-ferromagnets

This thesis presents a theoretical study of the Heisenberg model on a two dimensional lattice with asymmetric couplings along x and y directions. By gradually varying the coupling along y-direction we traverse the 1D, quasi 1D and 2D domains of this model. Primary focus of the research revolves around exploring the merits and de-merits of the staggered-flux state, a prototypical disordered resonating valance bond state, as a candidate wavefunction within this domain. Novel features like the fractionalization of spin-1 magnon' excitations into spin-1/2 spinon' excitations, which qualitatively explain the experimentally observed $(\pi,0)$ quantum anomaly, demand further investigation into this novel wave function.

Theoretical framework involving construction of a Gutzwiller projected staggered flux state, a wavefunction depending on variational parameters, is developed. A numerical method based on MonteCarlo simulation is used to optimize the variational wave function and calculate the relevant physical observables. Exploring the gradual evolution of these observables with the coupling ratio $\gamma=J_y/J_x$ provides us with a clear picture of the evolution of spin excitations on this RVB state, as the dimensionality of the model is changed from 1D to 2D.