Thermodynamics of frustrated spin lattices with flat bands

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The central goal of our project is the evaluation and subsequentanalysis of thermodynamic properties of frustrated quantum spin lattices for as big lattice sizes as possible. We are convinced that this is a unique opportunity since we could assemble the neccessary prerequisites in our team: long experience with frustrated quantum spin lattices, long experience with the finite-temperature Lanczos method (FTLM,) and last but not least direct access to the code spinpack. This code enables us to use the new supercomputer supermuc-ng at the Leibniz Supercomputing Center (LRZ) Garching with up to the Maximum number of nodes, 3076, i.e. 147,648 cores. We belong to those users who were given access prior to public use in order to test the machine. In particular, we want to investigate thermodynamic properties of the kagome lattice Heisenberg antiferromagnet (KHAF) for sizes N=45 and N=48 at the 1/3rd magnetization plateau in order to elucidate the phenomenon of asymmetric melting. Temperature and field dependent magnetization as well as the density of states will be studied. For lattice sizes of up to N=81 we want to study magnon crystallization on the KHAF, for which first investigations below the saturation field, i.e. at the 7/9 magnetization plateau, strongly point at a phase transition of the sameuniversality class as the two-dimensional 3-states Potts model. The magnon condensation suggested by a Japanese team for other magnetization plateaus, shall be investigated as well. We are convinced that they are of different origin. Our investigations shall be completed by similar studies for related frustrated spin systems that also possess flat bands, in particular the square kagome lattice and the planar pyrochlore lattice. Especially the square kagome lattice turned out to be an urgent problem since this structure could be synthesized quite recently and first experiments were published. During the last third of the project duration we would like to move away from a Heisenberg model towards XXZ couplings as well as next-nearest neighbor couplings in order to tune the frustration of the system as well as to deform the flat bands. This not only addresses realistic compounds, but should also help to understand the impact of specific frustration effects on e.g. magnetocaloric properties. Another issue along this line is the investigation how the spin quantum number influences the addressed properties.Besides comparing the various lattices, the J1-J2 square lattice throughout theproject will serve as reference system with tunable frustration. In addition, thermodynamic functions will be compared with an interpolation method that rests on high-temperature series expansions combined with a so-called entropy method.