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

Abstract

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...

Quantum dynamics and entanglement of spins on a square lattice

“…In addition, the two-magnon theory does not explain the momentum dependence of the amplitude of the longitudinal response, just as conventional spin-wave theory does not account for the amplitudes of the transverse response at the zone boundary. An alternative view is provided by the variational RVB approach (27,28), where the continuum above the zone boundary arises from fermionic (spinon) excitations. Unfortunately, no predictions have been made for the longitudinal continuum.…”

Single to Multiquasiparticle Excitations in the Itinerant Helical MagnetCeRhIn5

“…Such processes maybe determined by cubic terms in the Hamiltonian or possibly coupling resulting from the itinerant electronic nature of CeRhIn 5 as discussed elsewhere. [62][63][64][65] However, we note that in classical and insulating magnets the multiparticle continuum is weak comprising ∼ 1-2 % of the total spectral weight in Rb 2 MnF 4 . [60] The relatively large size of the multiparticle continuum in CeRhIn 5 suggests that localized effects are not the cause and that the itinerant properties are important.…”

Two-dimensionalXYbehavior observed in quasi-two-dimensional quantum Heisenberg antiferromagnets

“…Preliminary reports of this discovery led to several theoretical studies of the magnetization [13,14] and gave motivation for further investigations of the 2D QHAF in large applied fields. More recent papers [15,16] predict an anomalous spin excitation spectrum as the external field approaches H SAT . In addition, it has been predicted [17,18] that the application of an external field to a 2D QHAF would reduce quantum fluctuations along the field axis and gradually transform the spin anisotropy from Heisenberg toward XY , inducing a Berezinskii-Kosterlitz-Thouless (BKT) transition for perfectly isolated layers.…”