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arXiv:1909.00146 · Nature Physics

Dispersions of many-body Bethe strings

Anup Kumar Bera, Jianda Wu, Wang Yang, Robert Bewley, Martin Boehm, Jianhui Xu, Maciej Bartkowiak, O. Prokhnenko, Bastian Klemke, A. T. M. Nazmul Islam, Joseph Mathew Law, Zhe Wang, Bella Lake

Published Apr 6, 2020• 54 citations
arXivHTMLPDF
DOI
10.1038/s41567-020-0835-7

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Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​. In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​, and thus provide profound insight into many-body quantum magnetism.
Bethe strings are bound states of constituent particles in a variety of interacting many-body one-dimensional (1D) integrable quantum models relevant to magnetism, nanophysics, cold atoms and beyond. As emergent fundamental excitations, they are predicted to collectively reshape observable equilibrium and dynamical properties. Small individual Bethe strings have recently been observed in quantum magnets and superconducting qubits. However, creating states featuring intermixtures of many, including large, strings remains an outstanding experimental challenge. Here, using nearly integrable ultracold Bose gases, we realize such intermixtures of Bethe strings out of equilibrium, by dynamically tuning interactions from repulsive to attractive. We measure the average binding energy of the strings, revealing the presence of bound states of more than six particles. We find further evidence for them in the momentum distribution and in Tan's contact, connected to the correlated density. Our data quantitatively agree with predictions from generalized hydrodynamics (GHD). Manipulating intermixtures of Bethe strings opens new avenues for understanding quantum coherence, nonlinear dynamics and thermalization in strongly-interacting 1D systems.