Researchers Resolve Dispersion of Complex Quantum Many-Body States

In 1931, the theoretical physicist Hans Bethe had predicted complex magnon bound states in a one-dimensional (1D) quantum magnetic model.

In 2018, this theory of a “quantum string” was confirmed by physicist Dr Zhe Wang and his collaborators from the Institute of Physics II at the University of Cologne, for the first time. Dr Wang received the Walter Schottky Prize of the German Physical Society for his discovery.

In his present study, Dr Wang collaborated with researchers from Cologne, Berlin, Dresden, Didcot, Mumbai, Grenoble, Vancouver, and Shanghai to analyze the dispersion relation of “Bethe strings”—the complex quantum many-body states. Incidentally, the dispersion relation is known to be a major physical property. The researchers have reported their results in the Nature Physics journal.

Magnons are particle-like magnetic excitations, which occur separately in a quantum chain magnet and can also be coupled, creating a “string”-like excitation because of the complex quantum many-body effects.

Theoretical research works relating to quantum physics in 1D-systems have been much ahead of experimental studies. The reason for this is that a 1D-theoretical model can be more directly treated than higher-dimensional ones; however, it is not easy to achieve this in a real-world solid-state material.

Following Bethe’s seminal work, the so-called Bethe ansatz, or the systematic ansatz, has been created, which is a highly robust tool in the field of statistical physics to acquire the exact solutions of the 1D-models.

Through this technique, earlier theoretical research works demonstrated that in some 1D-models, the Bethe strings are almost impossible to detect by techniques including spectroscopic technique, because they play a very small in quantum dynamics.

The international research team achieved a couple of experimental breakthroughs. In 2018, the first proof of Bethe strings was demonstrated in SrCo2V2O8—a chain anti-ferromagnet—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. 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.

Dr Zhe Wang, Physicist, Institute of Physics II, University of Cologne

With the high-field terahertz spectroscopy, the researchers were able to detect the string states by accurately quantifying the typical field dependence of their eigen energies. But the optical spectroscopy cannot provide information on the dispersion of the string states in momentum space. “We need inelastic neutron scattering spectroscopy, for example,” added Dr Zhe Wang.

For the first time, the researchers resolved the dispersion of Bethe strings by performing inelastic neutron scattering experiments. Dispersion relation, that is, the relation between momentum and eigen energy, is a significant property of the excitations.

The effective measurements depend on high magnetic fields and high-quality single crystals at a neutron scattering facility, and both of these were recently realized by teams headed by Professor Bella Lake from the Helmholtz-Zentrum and the Technical University of Berlin.

Along with her collaborators, specifically, Dr Anup Kumar Bera, Professor Lake quantified the dispersion of the Bethe strings in high magnetic fields at the neutron scattering facilities.

Close collaboration between experimental and theoretical physicists is of particular importance for the achievements.

Dr Zhe Wang, Physicist, Institute of Physics II, University of Cologne

Using Bethe ansatz, Dr Jianda Wu, the Tsung-Dao Lee Fellow from Tsung-Dao Lee Institute at Shanghai Jiao Tong University, and Dr Wang Yang from the University of British Columbia in Vancouver, carried out accurate calculations of the 1D-model. The duo’s results allowed an in-depth comparison with the experimental data, and the detection 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.

Dr Zhe Wang, Physicist, Institute of Physics II, University of Cologne

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