We have developed a nonlocal functional of the exchange interaction for the ground-state energy of quantum spin chains described by the Heisenberg Hamiltonian. An alternating chain is used to obtain the correlation energy and a local unit-cell approximation is defined in the context of the density-functional theory. The agreement with our exact numerical data, for small chains, is significantly better than a previous formulation, even for chains with several ferromagnetic or antiferromagnetic bond defects. The results can be particularly relevant in the study of finite spin-1/2 Heisenberg chains, with exchange couplings changing, magnitude, or even sign, from bond-to-bond.
We study the effect of inhomogeneities of the lattice in the
S=1/2 bond-alternating chain by using a quantum Monte Carlo method and an exact diagonalization method. We adopt a defect in the alternating order as the inhomogeneity and we call it ``bond impurity.'' Local magnetic structures induced by the bond impurities are investigated both in the ground state and at very low temperatures. The local magnetic structure can be looked on as an effective
S=1/2 spin and the weakness of the interaction between the local structures causes the quasidegenerate states in the low energy. We also investigate the force acting between bond impurities and find that the force is generally attractive. We also study the dynamical property of the local magnetic structure. While the local magnetic structure behaves as an isolated
S=1/2 spin in the response to a time-dependent uniform field, it is found to be robust against the effect of noise applied at each site individually in the sweeping field.
We discuss one-dimensional(1D) spin compass model or 1D Kitaev model in the presence of local bond defects. Three types of local disorders concerning both bond-nature and bond-strength that occur on kitaev materials have been investigated. Using exact diagonalization, two-point spin-spin structural correlations and four-point Out-of-Time-Order Correlators(OTOC) have been computed for the defective spin chains. The proposed quantities give signatures of these defects in terms of their responses to location and strength of defects. A key observation is that the information in the OTOC space gets trapped at the defect site giving rise to the phenomena of localization of information thus making these correlators a suitable diagnostic tool to detect and characterize these defects.