The T=0 dynamics of the two-dimensional s=1/2 Heisenberg model with competing nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions is explored via the recursion method, specifically the frequency-dependent fluctuations of the order parameters associated with some of the known or suspected ordering tendencies in this system, i.e., Néel, collinear, dimer, and chiral order. The results for the dynamic structure factors of the respective fluctuation operators show a strong indication of collinear order at J2/J1≳0.6 and a potential for dimer order at 0.5≲J2/J1≲0.6, whereas the chiral ordering tendency is observed to be considerably weaker.The T=0 dynamics of the two-dimensional s=1/2 Heisenberg model with competing nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions is explored via the recursion method, specifically the frequency-dependent fluctuations of the order parameters associated with some of the known or suspected ordering tendencies in this system, i.e., Néel, collinear, dimer, and chiral order. The results for the dynamic structure factors of the respective fluctuation operators show a strong indication of collinear order at J2/J1≳0.6 and a potential for dimer order at 0.5≲J2/J1≲0.6, whereas the chiral ordering tendency is observed to be considerably weaker.

arXiv:cond-mat/9508145Journal of Applied PhysicsApr 15, 19960 citations

Quantum disordered vector-spin-chirality state in one dimensional Heisenberg model

Giuseppe Guarnaccia, Canio Noce

The European Physical Journal BSep 1, 20190 citations

Block spins and chirality in the frustrated Heisenberg model onkagome´ and triangular lattices

V. Subrahmanyam

The spin-1/2 frustrated Heisenberg model (HM) is investigated using a block-spin perturbation approach on kagome$aai--- and triangular lattices. In both cases, after coarse graining the triangles on the original lattice and truncation of the Hilbert space to the triangular ground-state subspace, HM reduces to an effective model on a triangular lattice in terms of the triangular-block degrees of freedom, viz. the spin and the chirality quantum numbers. The chirality part of the effective Hamiltonian captures the essential difference between the two lattices. It is seen that chiral-ordered variational states have high energies compared to the other variational states.The spin-1/2 frustrated Heisenberg model (HM) is investigated using a block-spin perturbation approach on kagome$aai--- and triangular lattices. In both cases, after coarse graining the triangles on the original lattice and truncation of the Hilbert space to the triangular ground-state subspace, HM reduces to an effective model on a triangular lattice in terms of the triangular-block degrees of freedom, viz. the spin and the chirality quantum numbers. The chirality part of the effective Hamiltonian captures the essential difference between the two lattices. It is seen that chiral-ordered variational states have high energies compared to the other variational states.

Physical review. B, Condensed matterJul 1, 199544 citations

Spin and charge fluctuations in the t–J model

George Jackeli, Nikolay M. Plakida

Physica B Condensed MatterJan 1, 19991 citation

Chiral mixed phase in disordered 3d Heisenberg models under magnetic fields

S. Belkhatir, Smain Bekhechi, Hamid Ez-zahraouy A

Physica A Statistical Mechanics and its ApplicationsJun 11, 20191 citation

Static and dynamical correlations in a spin-1/2 frustrated antiferromagnet

Didier Poilblanc, Eduardo R. Gagliano, Silvia Bacci +1 more

We study the frustrated spin-1/2 antiferromagnetic Heisenberg model on a square lattice of 16 sites, using a Lanczos algorithm and group-theoretical techniques. We investigate the competition between collinear, dimer, chiral, and spiral orders by calculating the dynamical and spatial correlation functions. Our numerical results strongly suggest the presence of long-range collinear order in the interval 0.55\ensuremath{\le} ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ \ensuremath{\le}0.9 (we cannot show numerically that this order exists for larger values of ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ ). Dimer- and chiral-order parameters both show increasing low-energy fluctuations and a longer range of the correlations in space around ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ \ensuremath{\sim}0.55. We propose an order parameter for chiral order exhibiting the full symmetry of the cluster and hence being less sensitive to finite-size effects. The mean value of the square of this plaquette chiral-order parameter is enhanced for ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ \ensuremath{\sim}0.55, where the characteristic chiral spin-fluctuation frequency is reduced, but no indications of long-range chiral order were found. Although the correlation function of the twist-order parameter is not a simple monotonically decreasing function of distance, little change is induced by frustration, suggesting that spiral order is not strongly favored. The energy gap corresponding to dimer order is smaller than those of spin waves, spiral order, and chiral order; thus, this state is the best candidate for an intermediate-( ${\mathit{J}}_{2}$ / ${\mathit{J}}_{1}$ ) phase in the ${\mathit{J}}_{1}$ - ${\mathit{J}}_{2}$ model.We study the frustrated spin-1/2 antiferromagnetic Heisenberg model on a square lattice of 16 sites, using a Lanczos algorithm and group-theoretical techniques. We investigate the competition between collinear, dimer, chiral, and spiral orders by calculating the dynamical and spatial correlation functions. Our numerical results strongly suggest the presence of long-range collinear order in the interval 0.55\ensuremath{\le}${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\le}0.9 (we cannot show numerically that this order exists for larger values of ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$). Dimer- and chiral-order parameters both show increasing low-energy fluctuations and a longer range of the correlations in space around ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\sim}0.55. We propose an order parameter for chiral order exhibiting the full symmetry of the cluster and hence being less sensitive to finite-size effects. The mean value of the square of this plaquette chiral-order parameter is enhanced for ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\sim}0.55, where the characteristic chiral spin-fluctuation frequency is reduced, but no indications of long-range chiral order were found. Although the correlation function of the twist-order parameter is not a simple monotonically decreasing function of distance, little change is induced by frustration, suggesting that spiral order is not strongly favored. The energy gap corresponding to dimer order is smaller than those of spin waves, spiral order, and chiral order; thus, this state is the best candidate for an intermediate-(${\mathit{J}}_{2}$/${\mathit{J}}_{1}$) phase in the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model.

Physical review. B, Condensed matterMay 1, 199143 citations

{\mathit{J}}_{2}

{\mathit{J}}_{1}

\ensuremath{\le}0.9 (we cannot show numerically that this order exists for larger values of

{\mathit{J}}_{2}

{\mathit{J}}_{1}

). Dimer- and chiral-order parameters both show increasing low-energy fluctuations and a longer range of the correlations in space around

{\mathit{J}}_{2}

{\mathit{J}}_{1}

\ensuremath{\sim}0.55. We propose an order parameter for chiral order exhibiting the full symmetry of the cluster and hence being less sensitive to finite-size effects. The mean value of the square of this plaquette chiral-order parameter is enhanced for

{\mathit{J}}_{2}

{\mathit{J}}_{1}

\ensuremath{\sim}0.55, where the characteristic chiral spin-fluctuation frequency is reduced, but no indications of long-range chiral order were found. Although the correlation function of the twist-order parameter is not a simple monotonically decreasing function of distance, little change is induced by frustration, suggesting that spiral order is not strongly favored. The energy gap corresponding to dimer order is smaller than those of spin waves, spiral order, and chiral order; thus, this state is the best candidate for an intermediate-(

{\mathit{J}}_{2}

{\mathit{J}}_{1}

) phase in the

{\mathit{J}}_{1}

{\mathit{J}}_{2}

model.