Singular spin-wave theory and scattering continua in the cone state of Cs₂CuCl₄

For temperatures below 0.6 K the geometrically frustrated layered quantum antiferromagnet Cs$_2$CuCl$_4$ in a magnetic field perpendicular to the layers orders magnetically in a so-called cone state, where the magnetic moments have a finite component in the field direction while their projection onto the layers forms a spiral. Modeling this system by a two-dimensional spatially anisotropic quantum Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interaction, we find that even for vanishing temperature the usual spin-wave expansion is plagued by infrared divergencies which are due to the coupling between longitudinal and transverse spin fluctuations in the cone state. Similar divergencies appear also in the ground state of the interacting Bose gas in two and three dimensions. Using known results for the correlation functions of the interacting Bose gas, we present a non-perturbative expression for the dynamic structure factor in the cone state of Cs$_2$CuCl$_4$. We show that in this state the spectral line shape of spin fluctuations exhibits singular scattering continua which can be understood in terms of the well-known anomalous longitudinal fluctuations in the ground state of the two-dimensional Bose gas.