Electrons inside a crystal exist in different states. In many cases it is the crystal structure that decides, if the material is a metal with a finite electric conductivity, or if it is an insulator, which does not carry an electric current. But there also exist insulating materials, whose crystal structures suggest that they should behave like metals. Such materials are called “Mott insulators”, and it is the repulsion between the electrons, that suppresses a metallic behaviour, such that the electrons are locked to the atoms.
The simulation of the quantum spin-liquid was performed on a flat honeycomb structure, where the electrons show a dynamical phase lacking any order.
Such localized electrons tend to order upon lowering the temperature, such as for example in magnetic structures. A “quantum spin-liquid” however is a non-magnetic Mott-insulator that is stabilized purely by quantum mechanical effects. The electrons inside a quantum spin-liquid resist to order down to the lowest temperatures, way down to the absolute zero of temperature at minus 273 degrees Celsius. The tendency to order is suppressed by dynamical fluctuations of the electrons even at zero absolute temperature (quantum fluctuations). For this to happen, the quantum fluctuations must be sufficiently large, which is rarely the case in nature, and also hard to realize in realistic models.
Now theorists from Stuttgart University, Zi Yang Meng, Priv.-Doz. Stefan Wessel, and Prof. Alejandro Muramatsu, together with their colleges Thomas Lang and Prof. Fakher Assaad from Würzburg University, showed that such a quantum spin-liquid exists in a realistic model of interacting electrons. For their study, they used large-scale computer simulations, in order to account for both the interactions between the electrons and their quantum fluctuations. Their unexpected findings were thus accepted for publication in the “Nature” magazine.
The quantum spin-liquid found by Meng et al. occurs in materials where the atoms form a two-dimensional, periodic array of hexagons, thus realizing a honeycomb lattice. Such a crystal structre is found for example in Graphene, a two-dimensional carbon allotrope, that was only recently synthesized, and has since then been the focus of intensive research. If the electronic interactions could be enhanced in such a material, then the highly interesting quantum spin-liquid state could be realized. It appears unlikly that this can be achieved, for example by expansion, in Graphene. Thus, the physicists from Stuttgart and Würzburg suggest exploring honeycomb-like structures formed from other group IV elements that show enhanced electronic interactions. A first step in this direction might already have been taken, since previously chemist succeeded in synthesizing Graphene-like structures of silicon atoms.
Furthermore, the quantum spin-liquid should also be realizable using ultra-cold atoms. In fact, the mathematical model studied by the physicists describes both interacting electrons in solid state systems as well as interacting ultra-cold atoms in an optical lattice. The impressive progress that has been achieved in this research field opens up the possibility to realize the quantum spin-liquid with ultra-cold atoms.
Another fascinating aspect of the quantum spin-liquid is that it can also be viewed as a starting point for superconductivity. Electric currents would then flow without resistance through the material. This has potential for many applications, such as ultra fast computers or the dissipation free transport of electricity.
In their fundamental research, the two theory groups in Stuttgart and Würzburg analyse complex phases of strongly interacting quantum many-body systems in general. They discovered the quantum spin-liquid phase, while studying possible transitions between metallic and insulating phases in a model for Graphene. In the vicinity of such transitions, the quantum fluctuations become significantly enhanced, and destroy any magnetic order. The scientists could also exclude other types of electronic orders from an extensive analysis. Such a study was only possible with the help of modern supercomputers. In particular, for their calculations, the theorists could profit from the highly efficient supercomputer centers in Jülich, München and Stuttgart. For the future, they hope to apply simulations of strongly interacting electrons also to the design of novel materials that realize exotic states of matter - including the quantum spin-liquid.
The research described above is embedded within the general research activities of the two universities. At the University of Stuttgart, the DFG research unit SFB/TRR 21, “Controll of Quantum Correlations in Tailored Matter“, focuses on the realization of tailored quantum systems. Its spokesperson is Prof. Tilmann Pfau from the University of Stuttgart. At the University of Würzburg, a recently established research group “Electron Correlation-Induced Phenomena in Surfaces and Interfaces with Tuneable Interactions“ complex electronic states are of central focus. Its spokesperson is Prof. Ralph Claessen from Würzburg University.