The phase diagram of a spin-1/2
J−J′−J2 model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the
J1−J2 model on the square lattice with two different nearest-neighbor couplings
J,J′ and may be also viewed as an array of coupled Heisenberg chains. The results suggest that the resonnating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B {\bf 67}, 024422 (2003)] for
J2=0.5J′≪J is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both side by a columnar dimer long range order. This columnar order could extends for
J′→J which correspond to the
J1−J2 model.
The phase diagram of a spin-1/2 $J\ensuremath{-}{J}^{\ensuremath{'}}\ensuremath{-}{J}_{2}$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the
J1−−J2 model on the square lattice with two different nearest-neighbor couplings ${J,J}^{\ensuremath{'}}$ and may also be viewed as an array of coupled Heisenberg chains. The results suggest that the resonating valence bond state predicted by Nersesyan and Tsvelik [Phys. Rev. B 67, 024422 (2003)] for ${J}_{2}{=0.5J}^{\ensuremath{'}}\ensuremath{\ll}J$ is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum. This line is likely bordered on both sides by a columnar dimer long range order. This columnar order could extend for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}J$ which correspond to the
J1−−J2 model.
In this publication I discuss the phase diagram of a frustrated spin-
21 Heisenberg model suggested in Nersesyan and Tsvelik, Phys. Rev. B 67, 024422 (2003). The phase diagram contains $(\ensuremath{\pi},0)$ and $(\ensuremath{\pi},\ensuremath{\pi})$ antiferromagnetic phases separated by the Valence Bond Crystal (VBC) state. I argue that the point of the phase diagram with deconfined spinons, predicted in the aforementioned work, is situated in the middle of VBC state, at the point where the dimerization order parameter changes sign.
Dynamical properties of frustrated XXZ models in the Ising limit on spatially anisotropic two-dimensional lattices are investigated by a weak-coupling approach from the one-dimensional limit. Restricting the Hilbert space to that spanned by exact eigenstates of XXZ chains in the Ising limit, we calculate dynamical structure factor 5 -+ (k,ω) in spatially anisotropic two-dimensional systems. As in the case of frustrated Heisenberg models [M.Kohno, et al. , Nat. Phys. 3, 790 (2007)], spinons form bound states through hopping process between chains. We calculate the density-density correlation function of spinons in the Ising limit, and show that spinons in the bound state hop together as a pair, although those in a continuous spectrum behave almost independently. We discuss possible implications of the present results on fractionalization of bosonic and fermionic particles in spatially anisotropic frustrated systems with strong repulsion.
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.