Doping Cycle - Dimensional Antiferromagnetic Heisenberg Model

The properties of the ground state and lower-energy excited state of the lower dimensional Antiferromagnetic Heisenberg(AFH) model has been one of the central areas of the theoretical research for many decades. In order to determine whether the AFH model can set up the Antiferromagnetic long-range order, the dimensionality of the system as one of the key factors is explored. In particular, the diverse situation of quasi-one-dimensional (QOD) systems due to their various geometric structures is further investigated.Through periodically doping spins(side spin) beside every spin site of the same sublattice of the one dimensional(lD) AFH linear chain, we construct a new class of QOD AFH spin model. The effective exchange integral for the interaction between the nearest neighbor spins on chain is J, and J is for the interaction between side spins and their nearest neighbor spin on chain.When = 1, the calculation by exact diagonalization shows that the side spins periodically doped in the same sublattice of a finite chain can effectively strengthen the spin-spin correlations in the large distance region, and make the tendency of the change to flat.By using Spin Wave theory and Green Function method, the effects of the side spins and the dimensionality of the system (with respect to the properties of the ground state and the lower-lying excitations) were analytically investigated.This new QOD model's properties differ greatly from the 1D AFH linear spin chain. There are three branches of excitation spectrum of the system: one is gapless and the other two are gapped. At lower temperatures, the specific heat of the system behaves like T1/2. There is no long-range order at finite temperature, which indicates that the Mermin-Wagner theorem can apply to this model.At ground state, there is magnetic long-range order when = 1, that is, side spins can set up magnetic long-range order when periodically adding side spins; while there is not when = 0. Obviously, with the changing of , there is a quantum phase transition in this system. According to our calculation, the critical point is at = 0.