The spin-1/2 antiferromagnetic Heisenberg chain with competing interactions

We investigate the thermodynamical and magnetic properties of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with competing interactions near the transition between the "dimer phase" and the "frustrated phase".     

Effects of the single-ion anisotropy and dimerization on 1D spin-1 antiferromagnetic Heisenberg chain

One-dimensional quantum spin-1 antiferromagnetic Heisenberg chain (AFHC) with exchange anisotropy J_z, dimerization δ and single-ion anisotropy D∑_n(S_n^z)² was investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the excitation spectrum, phase order and the phase fluctuation φ were derived in a self-consistent-harmonic-field approach. We studied the effects of the single-ion anisotropy and dimerization on two gaps by taking the different momentum cutoff α_i in two scalar field spaces H_i (i=1,2). The occurrences of richer phase transitions were understood in the viewpoints of the phase fluctuation and the z polar spin fluctuation. And the Gaussian critical line was given as J_z−D−πα₁δ=0.     

Exact analysis of ESR shift in the spin-1/2 Heisenberg antiferromagnetic chain

A systematic perturbation theory is developed for the ESR shift and is applied to the spin-1/2 Heisenberg antiferromagnetic chain with a general anisotropic exchange interaction. Using the Bethe ansatz technique, the resonance shift is obtained exactly for the whole range of temperature and magnetic field in the first order of the anisotropy. The obtained g shift strongly depends on magnetic fields at low temperature, showing a significant deviation from the previous classical result.     

Quantum phase diagram of a spin-1/2 antiferromagnetic chain with magnetic impurity

We present the renormalization group (RG) flow diagram of a spin-half antiferromagnetic chain with magnetic impurity and one altered link. In this two parameters (competing interactions) model, one can find the complex phase diagram with many interesting fixed points. There is no evidence of intermediate stable fixed point in weak coupling phase. It may arise at the strong coupling phase. Depending on the strength of couplings the phases correspond either to a decoupled spin with Curie law behavior or a logarithmically diverging impurity susceptibility as in the two channel Kondo problem.     

Entanglement in an anisotropic spin-1 Heisenberg chain

The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy \Delta and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearest-neighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.     

Calculation of correlation functions in the Heisenberg spin-1/2 antiferromagnetic model

We derive the exact expression of the four-spinon contribution S ₄ to the dynamical correlation function S of the spin 1/2 isotropic (XXX) He isenberg model in the antiferromagnetic regime using the quantum group symmetry of the model. We first give the exact expression for the n-spinon contribution in the form of contour integrals and display known results regarding the two-spinon contribution S ₂. Then we specialize the n-spinon formula to the case n = 4 and compute three sum rules for S ₄ that the total S is known to satisfy exactly. These are: the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that S ₄ corrects only by a small amount the contribution from S ₂. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Excitations in the antiferromagnetic Heisenberg chain

Non-singlet excitations of the antiferromagnetic Heisenberg chain of N atoms with spin $\text{1}\text{2}$ are examined. It is found that the energy of the lowest lying excitations for total spin S and wave number q converges to $\text{(}\text{π}\text{2}\text{)|}\text{sin}\text{q |}\text{as}\text{N → ∞,}\text{if only}\text{S?}\text{ln}\text{N}$.