We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form $\ensuremath{\omega}\ensuremath{\propto}{p}^{2}$ in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a three-dimensional weakly interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In two dimensions the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form $\ensuremath{\omega}\ensuremath{\propto}{p}^{2}$ in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a three-dimensional weakly interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In two dimensions the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.

arXiv:1712.00039Physical Review AMay 23, 201831 citations

Microscopic observation of magnon bound states and their dynamics

Takeshi Fukuhara, Peter Schauß, Manuel Endres +4 more

arXiv:1305.6598NatureSep 24, 2013459 citations

Magnon peak lineshape in the transverse dynamical structure factor of a magnetically polarized easy-axis $XXZ$ chain at low temperaturesMagnon peak lineshape in the transverse dynamical structure factor of a magnetically polarized easy-axis $XXZ$ chain at low temperatures

P. N. Bibikov

The ferromagnetically polarized gapped XXZ spin chain is studied at low temperatures. Utilizing only the one- and two-magnon spectrums and focusing on the magnon-creation contribution to the transverse dynamical susceptibility, we represent the latter in the form of the Dyson equation. Then, following the well known correspondence between the imaginary part of magnetic susceptibility and dynamical structure factor, we get the low-temperature formula for the magnon-peak lineshape. The suggested approach is effective only if the processes related to magnon creations and to transitions from magnons to coupled magnon pairs are energetically separated. As it is shown in the paper, such separation is inherent in the easy-axis chains with rather strong anisotropy. We present several plots and discuss their lineshapes. As the supplemental result we obtain integral representations for the temperature-dependent magnon resonance shift and the parameter which is usually associated with the decay rate. The low-temperature behavior of the resonance shift is studied in details. All calculations are performed up to {\it controllable} error $o({\rm e}^{-βE_{gap}})$ .The ferromagnetically polarized gapped XXZ spin chain is studied at low temperatures. Utilizing only the one- and two-magnon spectrums and focusing on the magnon-creation contribution to the transverse dynamical susceptibility, we represent the latter in the form of the Dyson equation. Then, following the well known correspondence between the imaginary part of magnetic susceptibility and dynamical structure factor, we get the low-temperature formula for the magnon-peak lineshape. The suggested approach is effective only if the processes related to magnon creations and to transitions from magnons to coupled magnon pairs are energetically separated. As it is shown in the paper, such separation is inherent in the easy-axis chains with rather strong anisotropy. We present several plots and discuss their lineshapes. As the supplemental result we obtain integral representations for the temperature-dependent magnon resonance shift and the parameter which is usually associated with the decay rate. The low-temperature behavior of the resonance shift is studied in details. All calculations are performed up to {\it controllable} error $o({\rm e}^{-βE_{gap}})$.

arXiv:2304.10645Apr 20, 20230 citations

Magnons in the Heisenberg model with a dynamical scaling symmetry

W.J. Caspers, Marian Kuźma, Barbara Lulek +1 more

Physica A Statistical Mechanics and its ApplicationsApr 1, 19984 citations

Magnon peak lineshape in the transverse dynamical structure factor of a magnetically polarized easy-axis

XXZ

chain at low temperatures

o({\rm e}^{-βE_{gap}})