Tensor Network Approach for the Two-Dimensional Kondo Lattice

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Two-dimensional strongly correlated electron systems are one of the most interesting classes of condensed matter theory. Here, strong quantum effects lead to fascinating states of matter such as for example non-Fermi liquid behavior, high-temperature superconductivity and collective order of charge and orbital degrees of freedom. Exotic magnetic phases appears especially if the geometry of the lattice is not compatible with the magnetic order. This effect is called geometrical frustration in technical language.The aim of the present research project is to investigate the magnetic properties of two-dimensional systems with electronic and magnetic degrees of freedom on geometrically frustrated lattice structures. To this end, a recent tensor network ansatz (the infinite projected entangled pair state (iPEPS) approach) will be applied to simulate the system numerically. Thereby, it is possible to incorporate the interactions between the particles accurately. The magnetism of such systems is in particular interesting because the electronic part acts as the mediator between the different magnetic constituents. The incorporation of geometrical frustration can thus lead to an interesting feedback on the electronic system. The computations will be performed for the triangular lattice as well as for a square lattice with additional diagonal links. Both lattice structures are not compatible with antiferromagnetic order and represent therefore frustrated systems. The obtained results will then be combined to gain a general understanding of the impact of geometrical frustration on the magnetism.The used model is the Kondo lattice and is designed for the qualitative description of the magnetic properties of heavy-fermion systems. Already existing experiments for these class of materials show indeed exotic magnetic states for compounds in which the underlying lattice is geometrically frustrated. The compound CePdAl represents a concrete example. The present research project should help to understand the qualitative mechanism for these exotic phases.