arXiv:cond-mat/0505458 · Physical Review B

Spin dynamics in the two-dimensional spin- 12 Heisenberg antiferromagnet

A. Fabricio Albuquerque, Antonio S. T. Pires, M. E. Gouvêa

Published Nov 22, 2005• 14 citations

Abstract

We present low-temperature dynamic properties of the quantum two-dimensional antiferromagnetic Heisenberg model with spin $S=1∕2$. The calculation of the dynamic correlation function is performed by combining a projection operator formalism and the modified spin-wave theory, which gives a gap in the dispersion relation for finite temperatures. The so calculated dynamic correlation function shows a double peak structure. We also obtain the spin-wave damping and compare our results to some experimental data and theoretical results obtained by other authors using different approaches.

DOI: 10.1103/physrevb.72.174423

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arXiv:cond-mat/0505458 · Physical Review B

Spin dynamics in the two-dimensional spin- 12 Heisenberg antiferromagnet

A. Fabricio Albuquerque, Antonio S. T. Pires, M. E. Gouvêa

Published Nov 22, 2005• 14 citations

arXiv HTML PDF

Abstract

We present low-temperature dynamic properties of the quantum two-dimensional antiferromagnetic Heisenberg model with spin

S=1∕2

. The calculation of the dynamic correlation function is performed by combining a projection operator formalism and the modified spin-wave theory, which gives a gap in the dispersion relation for finite temperatures. The so calculated dynamic correlation function shows a double peak structure. We also obtain the spin-wave damping and compare our results to some experimental data and theoretical results obtained by other authors using different approaches.

DOI: 10.1103/physrevb.72.174423

Related papers

Spin dynamics of the frustrated integer spin antiferromagnetic Heisenberg chain

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L.S. Lima

We present the low-temperature dynamic properties of the quantum one-dimensional Heisenberg antiferromagnet with integer Spin S with spin-phonon interaction, Dzyaloshins-kii-Moriya interaction and taking into account three magnon processes. First, we present the low-temperature dynamic properties of the quantum one-dimensionalHeisenberg antiferromagnet with integer spin S coupled to phonons. The calculation of the relaxation function is performed using the combination of the memory function formalism with the modified spin-wave theory. The procedure includes up to two-magnon and magnon-phonon processes. We show that the magnon-phonon coupling smooths the double-peak structure obtained for the model in the absence of phonons, when the wavevector q moves from q = ¼. After that, we present a calculation of the in-plane dynamical structure factor for the S = 1 one-dimensional antiferromagnet with a Dzyaloshinskii-Moriya interaction using the Schwinger boson mean-field theory. Then, we present the dynamical properties of the Heisenberg antiferromagnet takinginto account three magnon processes. We calculate the correlation function in time using the modified spin-wave theory. The procedure here includes up to two and three-magnon processes. We show that the double peak structure obtained for the model taking into account two-magnon processes is not smoothed when we take account three-magnon processes tooWe present the low-temperature dynamic properties of the quantum one-dimensional Heisenberg antiferromagnet with integer Spin S with spin-phonon interaction, Dzyaloshins-kii-Moriya interaction and taking into account three magnon processes. First, we present the low-temperature dynamic properties of the quantum one-dimensionalHeisenberg antiferromagnet with integer spin S coupled to phonons. The calculation of the relaxation function is performed using the combination of the memory function formalism with the modified spin-wave theory. The procedure includes up to two-magnon and magnon-phonon processes. We show that the magnon-phonon coupling smooths the double-peak structure obtained for the model in the absence of phonons, when the wavevector q moves from q = ¼. After that, we present a calculation of the in-plane dynamical structure factor for the S = 1 one-dimensional antiferromagnet with a Dzyaloshinskii-Moriya interaction using the Schwinger boson mean-field theory. Then, we present the dynamical properties of the Heisenberg antiferromagnet takinginto account three magnon processes. We calculate the correlation function in time using the modified spin-wave theory. The procedure here includes up to two and three-magnon processes. We show that the double peak structure obtained for the model taking into account two-magnon processes is not smoothed when we take account three-magnon processes too

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Spin excitation spectra of the two-dimensional S=12 Heisenberg model with a checkerboard structure

Yining Xu, Zijian Xiong, Han-Qing Wu +1 more

We study the spin excitation spectra of the two-dimensional spin- $\frac{1}{2}$ Heisenberg model with a checkerboard structure using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions ${J}_{1}$ and ${J}_{2}$ , and the tuning parameter $g$ is defined as ${J}_{2}/{J}_{1}$ . The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When $g$ is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when $g$ is small. The gapless branch in this case can be regarded as a spin wave in N\'eel order formed by a ``block spin'' in each $3\ifmmode\times\else\texttimes\fi{}3$ plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.We study the spin excitation spectra of the two-dimensional spin-$\frac{1}{2}$ Heisenberg model with a checkerboard structure using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions ${J}_{1}$ and ${J}_{2}$, and the tuning parameter $g$ is defined as ${J}_{2}/{J}_{1}$. The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When $g$ is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when $g$ is small. The gapless branch in this case can be regarded as a spin wave in N\'eel order formed by a ``block spin'' in each $3\ifmmode\times\else\texttimes\fi{}3$ plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.

arXiv:1811.12753Physical review. B./Physical review. BFeb 7, 201917 citations

We present low-temperature dynamic properties of the quantum two-dimensional antiferromagnetic Heisenberg model with spin

S=1∕2

{\mathrm{La}}_{2}

{\mathrm{CuO}}_{4}

. The low-energy sector exhibits scaling behavior with the characteristic frequency scale, which is inversely proportional to the correlation length.

The dynamical correlation function

{\mathit{G}}_{\mathbf{r}}

(t)==〈

{\mathbf{S}}_{\mathbf{r}}

(t)\ensuremath{\cdot}

{\mathbf{S}}_{0}

(0)〉 and dynamical structure factor

{\mathit{S}}_{\mathbf{q}}

(\ensuremath{\omega}) are calculated by the modified spin-wave theory for the low-dimensional quantum Heisenberg ferromagnets at low temperature. We use the Dyson-Maleev transformation, ideal spin-wave states, and the rotational averaging.

{\mathit{S}}_{\mathbf{q}}

(\ensuremath{\omega}) satisfies the dynamic scaling relation. The explicit form of the scaling function is obtained. The classical limit of our results is compared with a molecular-dynamics calculation. The agreement is surprisingly good.

We study the spin excitation spectra of the two-dimensional spin-

\frac{1}{2}

Heisenberg model with a checkerboard structure using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions

{J}_{1}

and

{J}_{2}

, and the tuning parameter

g

is defined as

{J}_{2}/{J}_{1}

. The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When

g

is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when

g

is small. The gapless branch in this case can be regarded as a spin wave in N\'eel order formed by a ``block spin'' in each $3\ifmmode\times\else\texttimes\fi{}3$ plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.