The one-dimensional S =1 anisotropic antiferromagnetic Heisenberg model with next-nearest as well as nearest-neighbor exchange intearction is studied with particular emphasis on the effect of the frustration. The ground-state phase diagram and the low-lying excitations are examined by use of the bosonization method and the self-consistent harmonic approximation. It turns out that the frustration works in stabilizing the Haldane phase against the Neel phase, since its effect on the latter phase is larger. The large- D phase is almost unaffected by the frustration, resulting in its relative stability against other phases. The excitation gap in the Haldane phase (Haldane gap) is found to be reduced by the frustration near the boundary to the large- D phase, while it increases in the vicinity of the Neel phase.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(F)(1)) and antiferromagnetic (J(A)(1)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(F)(2)). In this model frustration is present due to the non-zero J(F)(2). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(F)(2)and large J(F)(1)/J(A)(1). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(F)(1), the phase diagram in the space of J(A)(1)-J(F)(2) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(1)(F)) and antiferromagnetic (J(1)(A)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(2)(F)). In this model frustration is present due to the non-zero J(2)(F). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(2)(F) and large J(1)(F)/J(1)(A). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(1)(F), the phase diagram in the space of J(1)(A)-J(2)(F) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
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 excitation spectrum is studied around the degenerate point at the Ising limit in the one-dimensional anisotropic Heisenberg antiferromagnets with next-nearest-neighbor interactions. Solitons are found as propagation modes in the N\'eel state and in the (2,2) antiphase state, while triplet-dimer excitations are found propagating in the dimer state. These excitations determine the shape of dynamical spin-correlation functions, which are calculated by an exact diagonalization for finite chains. The phase diagram is determined from the condition that the energy gap vanishes in the excitation spectrum.
We study the
S=1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor couplings
J1x and
J1y frustrated by a next-nearest-neighbor coupling
J2 numerically using the density-matrix renormalization-group (DMRG) method and analytically employing the Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the N\'eel-ordered state above the classically stable region. Whereas SBMFT suggests a fluctuation-induced first-order transition between the N\'eel state and a stripe antiferromagnet for $1/3\ensuremath{\le}{J}_{1x}/{J}_{1y}\ensuremath{\le}1$ and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum-disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for
S=1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.