We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.
Abstract A quantum spin model of a delta chain with exchange interactions of ferro- (F) and antiferromagnetic (AF) types is studied. The model properties significantly depend on the frustration parameter α (the ratio of the constants of AF and F interactions). When α < 1/2, the ground state is ferromagnetic, and at α = 1/2, a quantum phase transition occurs to another phase. Based on the numerical calculations and analysis of the model at large values of α it is concluded that the ground state at α > 1/2 is magnetically ordered and the total spin of the ground state is half the maximum possible spin. Comparison of the properties of the ground state of the classical and quantum models shows that the considered model is an example of a system in which quantum effects are responsible for the appearance of order from disorder.
We study the long-range behavior of spin correlations in low-dimensional spin-1/2 antiferromagnets with both Ising anisotropy and spatial anisotropy. We represent the spin operators in terms of spin-density operators and spin-phase operators. Then for spin-1/2 antiferromagnets, within a simple harmonic approximation, we obtain expressions for the spin correlations in the ground state. For the one-dimensional linear chain, we find that the two leading terms in spin correlation are (-1
)rc/${\mathit{r}}^{\mathrm{\ensuremath{\eta}}}$-
c1/
r2 for large distance r. The power \ensuremath{\eta} depends on the Ising anisotropy, and \ensuremath{\eta}=0.405 at XY point and \ensuremath{\eta}=1.062 at Heisenberg point. For the two-dimensional square lattice, there is long-range staggered magnetization, and the dependence of magnetization on Ising anisotropy is given. For the crossover from one-dimensional linear chain to two-dimensional square lattice, we find that the disorder-order transition occurs as long as the interchain coupling is introduced. We believe that our method gives a unified approach to the long-range behavior of spin correlations in low-dimensional spin-1/2 antiferromagnets.
Numerical calculations of quantum-mechanical time correlation functions are reported for finite Heisenberg linear chains containing up to 10 spin-\textonehalf{} particles. The results, obtained by manipulation of eigenvalues and eigenfunctions, give Fourier transforms in histogram form. Two-spin correlation functions show a sharp rise near zero frequency and highly non-Gaussian behavior at infinite temperature. The short-time behavior is estimated and compared with classical calculations and other theories. Four-spin functions are calculated and compared with results of a simple decoupling approximation. Spatial Fourier transforms of two-spin functions as needed for neutron scattering cross sections are computed. These are limited to fairly short wavelengths by the finiteness of the system. The temperature dependence of two-spin functions shows a decrease in the near-zero frequency component with decreasing temperature. Computed correlation functions are used to predict the frequency dependence of the ESR linewidth in the linear-chain salt
Cu(NH3)4S
O4\ifmmode\cdot\else\textperiodcentered\fi{}
H2O, and comparison is made with experiment. Very good agreement is found using the same exchange constant
J as inferred from specific-heat and magnetic-susceptibility data. The Gaussian approximation, on the other hand, is in extremely poor agreement.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (
J1F) and antiferromagnetic (
J1A) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (
J2F). In this model frustration is induced by the non-zero
J2F and the effect of dimerization is realized by changing the strength of
J1A for a fixed value of
J1F. The model with site spin
s behaves like a Haldane spin chain with site spin 2
s in the limit of vanishing
J2F and large
J1F/J1A. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of
J1A−J2F is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
The excitations of the Heisenberg antiferromagnetic spin chain in zero field are known as spinons. As pairwise-created fractionalized excitations, spinons are important in the understanding of inelastic neutron scattering experiments in (quasi-)one-dimensional materials. In the present paper, we consider the real space-time dynamics of spinons originating from a local spin flip on the antiferromagnetic ground state of the (an)isotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model. By utilizing algebraic Bethe ansatz methods at finite system size to compute the expectation value of the local magnetization and spin-spin correlations, spinons are visualized as propagating domain walls in the antiferromagnetic spin ordering with anisotropy dependent behavior. The spin-spin correlation after the spin flip displays a light cone, satisfying the Lieb-Robinson bound for the propagation of correlations at the spinon velocity.