# Many quantum particles

Quantum materials have attracted much interest during the past decades. Putting a large number of identical quantum particles together induces a wide range of new and often unexpected physical phenomena. Due to their quantum nature, the interactions of these particles lead to the emergence of new states, new phases, new excitations, new physical laws and principles. This is particularly true for correlated electrons in solids, being at the heart of our theoretical research.

Currently, the state of research is shifting towards “controlling” these exotic phase transitions with a long-term goal of applying them in future new-principle electronics. Our in-house experimental colleagues are providing us with new ideas in doing so. They are able to engineer new states by creating devices working in the hydrodynamic/nonequilibrium regime, inducing superconductivity and magnetism by applying external fields or strains, and even creating new materials.

We focus on many-body effects, ordering phenomena, and collective excitations in strongly correlated electron systems in and out of equilibrium. Of special interest are nonequilibrium states induced by external electric fields in nonlinear devices. We have proposed how to obtain Floquet topological states, nonequilibrium Mott transitions and a negative temperature state, while some of them are already experimentally realized. It is our research target to find even more of such exotic quantum phenomena. In addition to charge degrees of freedom, we are interested in magnetic ordering and spin dynamics due to their importance in information storage and processing. Characteristic features can also be seen in the temperature and field dependence of thermodynamic quantities like heat capacity, magnetic susceptibility, magnetization, and the magnetocaloric effect.

To investigate these effects, we develop and use various theoretical methods, including nonequilibrium many-body perturbation theory, and the finite temperature Lanczos algorithm. Our goal is to derive a detailed understanding of the materials we are exploring. To this end we work closely together with our experimental colleagues as well as with theoretical and experimental groups worldwide. A strong overlap and intense cooperation also exists with the theorists from our departments as well as with the neighboring Max Planck Institute for the Physics of Complex Systems.

**Further readings: **

*Photovoltaic Hall effect in graphene*; T. Oka, and H. Aoki, Phys. Rev. B**79**, 081406(R) (2009).*Evidence for hydrodynamic electron flow in PdCoO*; P.J.W. Moll, P. Kushwaha, N. Nandi, B. Schmidt, and A.P. Mackenzie, arXiv:1509.05691._{2}*Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange*, B. Schmidt and P. Thalmeier, New J. Phys. 17, 073025 (2015). MPG.PuRe*Exploring the spin-(1/2) frustrated square lattice model with high-field magnetization studies*, A.A. Tsirlin, B. Schmidt, Y. Skourski et al., Phys. Rev. B 80, 132407 (2009).MPG.PuRe- Burkhard Schmidt: Theory of quantum materials
- Takashi Oka: Nonequilibrium quantum matter

**Figures:**

*Figure 1:*Temperature dependence of the static magnetic susceptibility χ(T) of Cs

_{2}CuCl

_{4}(dots and solid line) and Cs

_{2}CuBr

_{4}(open circles and dashed line). The symbols represent the experimental data, the lines are results from our FTLM calculations based on the anisotropic Heisenberg model on the triangular lattice. The agreement is excellent, demonstrating that the frustration effects inherent to the model dominate the thermodynamic and magnetocaloric properties of the class of materials the two compounds chosen represents.

*Figure 2:*The measured resistivity of PdCoO

_{2}channels normalized to that of the widest channel (ρ

_{0}), plotted against the inverse channel width 1/W multiplied by the bulk momentum- relaxing mean free path ℓ

_{MR}(closed black circles). Plotted in this dimensionless form, the prediction of a standard Boltzmann theory including boundary scattering but neglecting momentum-conserving collisions (blue solid line) has no free parameters. It is seen to be a poor match to experiment both in magnitude and functional form. The red line is a prediction of a model that includes the effects of momentum-conserving (hydrodynamic) scattering. It is seen to be a good match to the data, providing evidence that hydrodynamic effects play an important role in transport in PdCoO

_{2}

*Figure 3:*(Left) Honeycomb lattice in circularly polarized laser becomes a Floquet Chern insulator.

(Right) The Floquet quasi-energy in the high frequency limit shows a gap opening at the Dirac points. This leads to the emergence of the Chern density. If the lower Floquet band is fully occupied, the Floquet-Chern number would be one.