News Release 

Dispersion of the quantum many-body states 'Bethe Strings' experimentally resolved

University of Cologne

Complex magnon bound states were predicted in 1931 by the theoretical physicist Hans Bethe in a one-dimensional quantum magnetic model. In 2018, physicist Dr Zhe Wang and his colleagues at the University of Cologne's Institute of Physics II confirmed this theory of a 'quantum string' for the first time. For his discovery, he was awarded the Walter Schottky Prize of the German Physical Society.

In his current work, Wang cooperated with scientists from Berlin, Cologne, Didcot, Dresden, Grenoble, Mumbai, Shanghai, and Vancouver to explore the dispersion relation - an important physical characteristic - of the complex quantum many-body states 'Bethe strings'. The team reported their results in the journal Nature Physics.

Magnons - particle-like magnetic excitations - exist not only independently in a quantum chain magnet, but can also be bound forming a 'string'-like excitation due to quantum many-body effects. Theoretical studies of quantum physics in one-dimensional systems have been way ahead of an experimental one. This is because a one-dimensional theoretical model can be more straightforwardly treated than higher-dimensional ones, but it is difficult to realize in a real-world solid-state material. After Bethe's seminal work, a systematic ansatz - the so-called Bethe ansatz - has been developed which is a very powerful tool in statistical physics to obtain exact solutions of the one-dimensional models. Using this method, previous theoretical studies showed that in certain one-dimensional models the Bethe strings are hardly detectable, e.g. by a spectroscopic method, because their contribution to quantum dynamics is negligibly small.

Two experimental breakthroughs have been achieved by the international research team. First evidence of Bethe strings was revealed in 2018 in a chain antiferromagnet, SrCo2V2O8, by high-resolution terahertz optical spectroscopy in applied external high magnetic fields. 'The external field plays a crucial role. Only in a field-induced gapless phase of the chain antiferromagnet we found the Bethe string states', said Dr Zhe Wang. 'This particular phase was rarely explored before, because neither a solid-state antiferromagnetic chain material nor the required strong magnetic field is easy to obtain.' The high-field terahertz spectroscopy allowed the team to identify the string states by precisely measuring characteristic field dependence of their eigenenergies. However, information on dispersion of the string states in momentum space cannot be provided by the optical spectroscopy. 'We need inelastic neutron scattering spectroscopy, for example', Zhe Wang added.

The team resolved the dispersion of Bethe strings for the first time by inelastic neutron scattering experiments. Dispersion relation - a relation between eigenenergy and momentum - is an important characteristic of the excitations. The successful measurements rely on high-quality single crystals and high magnetic fields at a neutron scattering facility, both of which were achieved recently by groups led by Professor Bella Lake from the Helmholtz-Zentrum and Technical University of Berlin. With her colleagues, in particular Dr Anup Kumar Bera, she measured dispersion of the Bethe strings in high fields at the neutron scattering facilities.

'Close collaboration between experimental and theoretical physicists is of particular importance for the achievements', said Zhe Wang. Precise calculations of the one-dimensional model were performed by the Tsung-Dao Lee Fellow Dr Jianda Wu from Tsung-Dao Lee Institute at Shanghai Jiao Tong University and Dr Wang Yang from the University of British Columbia in Vancouver using Bethe ansatz. Their results enabled a detailed comparison to the experimental data, and the identification of the string-states dispersion.

'Quantum many-body systems are in general challenging to study, while at the same time exotic and fascinating phenomena are realized in these systems. To explore these phenomena is an important goal of my research. In the long term, understanding these phenomena might lead to invention of new quantum technologies', Zhe Wang concluded.

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