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arXiv:cond-mat/0309408 · Physical Review Letters

Dynamic Structure Factor of the Two-Dimensional Shastry-Sutherland Model

Christian Knetter, Götz Silvester Uhrig

Published Jan 16, 2004• 48 citations
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Abstract

We calculate the two-triplon contribution to the dynamic structure factor of the two-dimensional Shastry-Sutherland model, realized in SrCu2(BO3)(2), by means of perturbative continuous unitary transformations. For realistic parameters we find flat bound two-triplon bands. These bands show large weight in the structure factor depending strongly on momentum. So our findings permit a quantitative understanding of high precision inelastic neutron scattering experiments.

DOI
10.1103/physrevlett.92.027204

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We calculate the two-triplon contribution to the dynamic structure factor of the two-dimensional Shastry-Sutherland model, realized in SrCu2(BO3)(2), by means of perturbative continuous unitary transformations. For realistic parameters we find flat bound two-triplon bands. These bands show large weight in the structure factor depending strongly on momentum. So our findings permit a quantitative understanding of high precision inelastic neutron scattering experiments.
In this letter we report on the high energy-resolution neutron scattering studies on the dynamic structure factor of the two-triplet bound states in the two-dimensional S = 1/2 Shastry–Sutherland system, SrCu 2 (BO 3 ) 2 , in the energy transfer range of 4 to 7 meV. In contrast to the earlier interpretation of the low energy-resolution results, these bound state excitations show hardly any dispersion, but do show a strong wave-vector-dependent structure factor. Although these findings are in overall agreement with the recent theoretical calculation of the 2-triplon dynamic structure factor by Knetter and Uhrig [Phys. Rev. Lett. 92 (2004) 027204], they also show distinct differences, which may be due to some symmetry-breaking terms in the Hamiltonian that are not included in the theory, such as the interdimer Dzyaloshinski–Moriya interactions recently discovered in this compound.
Motivated by the remarkable properties of SrCu2(BO3) 2 in a magnetic field, we use perturbative continuous unitary transformations to determine the magnetization plateaux of the Shastry-Sutherland model, unveiling an unexpected sequence of plateaux progressively appearing at 2/9, 1/6, 1/9, and 2/15 upon increasing the interdimer coupling. We predict that a 1/6 plateau should be present in SrCu2(BO3)2, even if residual interactions beyond the Shastry-Sutherland are strong enough to modify the other plateaux below 1/3. The method is extended to calculate the magnetization profile within the plateaux, leading to a local structure around triplons that agrees with NMR results on SrCu2(BO3) 2.
In the quantum magnet SrCu2(BO3)2, an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap A using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in SrCu2(BO3)2 are captured by the spin S = 1/2 Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper [Phys. Rev. B 113, 024406 (2026)]. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap A to the single triplon excitations at the experimentally relevant model parameters.
Anomalous thermal broadening in the Shastry-Sutherland model and SrCu2(_2(2​(BO3)2_3)_23​)2​
The quantum magnet SrCu2(_2(2​(BO3)2_3)_23​)2​ and its remarkably accurate theoretical description, the spin-1/21/21/2 Shastry-Sutherland model, host a variety of intriguing phenomena such as a dimer ground state with a nearly flat band of triplon excitations, a series of magnetization plateaux, and a possible pressure-induced deconfined quantum critical point. One open puzzle originating from inelastic neutron scattering and Raman experiments is the anomalous broadening of the triplon modes at relatively low temperatures compared to the triplon gap ΔΔΔ. We demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. To this end, we develop a numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately. Perturbative calculations identify the origin of this phenomenon as a small energy scale compared to ΔΔΔ between single triplon and bound triplon states at the experimentally relevant model parameters.
In the quantum magnet SrCu 2 ( BO 3 ) 2 , an anomalous thermal broadening of the triplon modes has been measured at relatively low temperatures compared to the triplon gap Δ using both inelastic neutron scattering and Raman spectroscopy. Given how accurately a broad variety of physical phenomena in SrCu 2 ( BO 3 ) 2 are captured by the spin S = 1 / 2 Shastry-Sutherland model, it remains an open question whether the anomalous thermal broadening is also an intrinsic feature of this minimal model. However, few techniques are available for computing the finite-temperature dynamics of strongly interacting many-body systems. To address this problem, we have developed a broadly applicable numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately, detailed in a companion paper []. Using this technique, we demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. Perturbative calculations identify the origin of this phenomenon as singlet bound two-triplon states being thermally excited at an energy scale small compared to the gap Δ to the single triplon excitations at the experimentally relevant model parameters.
We study an extended Shastry-Sutherland model for SrCu2(BO3)2 and analyze the low lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations.The derivation of the 1-magnon dispersion (elementary triplets) is discussed.Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets.Our high order results allow to fix the model parameters for SrCu2(BO3)2 precisely: J1 = 6.16(10)meV, x := J2/J1 = 0.603(3), J ⊥ = 1.3(2)meV.To our knowledge this is the first quantitative treatment of bound states in a true 2d model.