Spin waves in the flux-phase description of the<i>S</i>=1/2 Heisenberg antiferromagnet

Hsu, T. C.

doi:10.1103/physrevb.41.11379

Cited by 99 publications

(109 citation statements)

References 27 publications

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“…We think, however, that a triplon picture which includes the interactions on the quantitative level can give a good description of the Raman response. A similar treatment in terms of gapped quasiparticles already led to an improved agreement between theory and experiments 78,79 .…”

Section: Cuprate Planesmentioning

confidence: 94%

Raman response of magnetic excitations in cuprate ladders and planes

et al. 2005

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An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J and J ⊥ plus an additional four-spin interaction Jcyc. Within this model Sr123 and Sr14 can be described by x := J /J ⊥ = 1.5, xcyc := Jcyc/J ⊥ = 0.2, J Sr123 ⊥ = 1130 cm −1 and J Sr14 ⊥ = 1080 cm −1 . The couplings found for La6Ca8 are x = 1.2, xcyc = 0.2, and J La6Ca8 ⊥ = 1130 cm −1 . The unexpected sharp two-triplon peak in the ladder materials compared to the undoped two-dimensional cuprates can be traced back to the anisotropy of the magnetic exchange in rung and leg direction. With the results obtained for the isotropic ladder we calculate the Raman line-shape of a two-dimensional square lattice using a toy model consisting of a vertical and a horizontal ladder. A direct comparison of these results with Raman experiments for the two-dimensional cuprates R2CuO4 (R=La,Nd), Sr2CuO2Cl2, and YBa2Cu3O 6+δ yields a good agreement for the dominating two-triplon peak. We conclude that short range quantum fluctuations are dominating the magnetic Raman response in both, ladders and planes. We discuss possible scenarios responsible for the high-energy spectral weight of the Raman line-shape, i.e. phonons, the triple-resonance and multi-particle contributions.

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Section: Cuprate Planesmentioning

confidence: 94%

Raman response of magnetic excitations in cuprate ladders and planes

et al. 2005

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“…This magnetic ordering produces a gap for the spinons. Such a mean field description of the antiferromagnetic state was first proposed by Hsu 32 . Similar ideas have subsequently been explored in a number of publications -see Refs.…”

Section: Introductionmentioning

confidence: 99%

Néel order, quantum spin liquids, and quantum criticality in two dimensions

Ghaemi

Senthil

2006

Phys. Rev. B

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This paper is concerned with the possibility of a direct second order transition out of a collinear Neel phase to a paramagnetic spin liquid in two dimensional quantum antiferromagnets. Contrary to conventional wisdom, we show that such second order quantum transitions can potentially occur to certain spin liquid states popular in theories of the cuprates. We provide a theory of this transition and study its universal properties in an ǫ expansion. The existence of such a transition has a number of interesting implications for spin liquid based approaches to the underdoped cuprates. In particular it considerably clarifies existing ideas for incorporating antiferromagnetic long range order into such a spin liquid based approach.

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“…This dispersion, which also has been confirmed using Monte Carlo simulations [2], shows a broad shallow minimum around (0, π). This feature which is not captured within linear spin wave theory (LSW) is reminiscent of a prediction made by Hsu [3]. Treating the Heisenberg model in an approximation involving massive fermions, he found a rather deep minimum in the dispersion at (0, π).…”

mentioning

confidence: 88%

“…The projection of this state gives long range Neel order with a sublattice magnetization which is in excellent ageement with exact computations. [3] Thus we are led to consider an effective Hamiltonian whose mean field solution gives the π-flux state with the spin density wave. This is accomplished by introducing a weak on-site repulsion V. The value of V is to be determined variationally to produce the proper magnetization and should not be confused with the original strong Hubbard U.…”

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confidence: 99%

Anomalous Spin Excitation Spectrum of the Heisenberg Model in a Magnetic Field

Syljuåsen

Lee

2002

Phys. Rev. Lett.

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Making the assumption that high energy fermions exist in the two dimensional spin-1/2 Heisenberg antiferromagnet we present predictions based on the π-flux ansatz for the dynamic structure factor when the antiferromagnet is subject to a uniform magnetic field. The main result is the presence of gapped excitations in a momentum region near (π, π) with energy lower than that at (π, π). This is qualitatively different from spin wave theory predictions and may be tested by experiments or by quantum Monte Carlo. PACS numbers: 75.10Jm, 71.10Pm, 74.20Mn It is well known in particle physics that the nature of elementary excitations for one and the same model might change as different momenta-and energy-scales are probed. In particular, mesons at very high energies are best described as pairs of fermions (quarks) while at low energies they are bosons. It has been suggested that a similar possibility exists in the Heisenberg spin-1/2 antiferromagnet on a square lattice, where the low energy excitations are Goldstone bosons while the high energy excitations show features more resembling fermions (loosely called spinons in the literature). Taking this as a real possibility we describe here the consequences of adding a magnetic field to the model in order to bring out clearly the signatures of the underlying high energy fermions. The predictions made in this paper can be tested experimentally in materials such as copper formate tetra-deuterate (CFTD) or the organic compound (5CAP)2CuBr4 where the exchange constant is not too large. They can also be tested using numerical tools such as quantum Monte Carlo.The recently observed dispersion along the antiferromagnetic zone boundary (π/2, π/2)-(0, π) (lattice spacing is set to unity throughout this Letter) in experiments on CFTD[1] is an indication that the nature of high-energy excitations in the Heisenberg model might be different from the low energy ones. This dispersion, which also has been confirmed using Monte Carlo simulations[2], shows a broad shallow minimum around (0, π). This feature which is not captured within linear spin wave theory (LSW) is reminiscent of a prediction made by Hsu[3]. Treating the Heisenberg model in an approximation involving massive fermions, he found a rather deep minimum in the dispersion at (0, π). While this minimum seems much to deep to explain the experiments, Ho et al. [4] recently calculated the full dynamic structure factor using the same fermionic picture. They showed that the pole at (0, π) merges with an extensive high-energy continuum carrying lots of spectral weight. For experiments this implies that the spectral peak at (0, π) would be very broad and an accurate determination of the magnon energy would be difficult, if anything, the high-energy continuum would make the dispersion appear shallower than in Hsu's original prediction.Neutron scattering is necessarily an indirect probe of spin-1/2 fermions as it measures spin-1 excitations. So in order to establish the existence of fermionic excitations it appears that one nee...

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Spin waves in the flux-phase description of theS=1/2 Heisenberg antiferromagnet

Cited by 99 publications

References 27 publications

Raman response of magnetic excitations in cuprate ladders and planes

Raman response of magnetic excitations in cuprate ladders and planes

Néel order, quantum spin liquids, and quantum criticality in two dimensions

Anomalous Spin Excitation Spectrum of the Heisenberg Model in a Magnetic Field

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