Theoretical Solid State Physics

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(Fermionic) Tensor network states in symmetric multi-band Hubbard and Heisenberg models

We have an opening for a two-year postdoc position in computational condensed matter theory at the Ludwig-Maximilians-University in Munich, Germany, funded by DFG/WE4819-3 with starting date early fall 2017.

The focus of the project is on the detailed exploration of the phase diagrams of symmetric multi-flavor fermionic Hubbard models at arbitrary chemical potential as well as Heisenberg models on two dimensional (2D) lattice geometries using tensor network states. In particular, this includes superconducting properties at finite doping, as well as the role of Hund's coupling on the correlated interplay of spin and orbital degrees of freedom (cf. iron pnictides).

Based on the existing QSpace tensor library [1], we have the tools to fully exploit the underlying non-abelian symmetries in quasi-1D [density matrix renormalization group (DMRG) on ladders and cylinders] as well as truely 2D tensor networks (projected entangled pair states, PEPS). By constraining ourselves to degenerate symmetric bands, this allows us to go significantly beyond the current state of the art in numerical simulations of multi-flavor models. Very promising early work on the application of SU(2) in 2D-PEPS includes the spin-1 Kagome lattice [2], with first successful ongoing tests on fermionic PEPS in 2D fully exploiting SU(2) and SU(3) symmetries. Note that QSpace allows us to turn on and off abelian and non-abelian symmetries at will. Currently accessible symmetries include arbitrary combinations of U(1), Z_n, SU(N<=5), as well as Sp(2N<=8) symmetries.

The successful applicant is expected to have a strong proven record of numerical expertise on tensor network states, and preferentially already also experience with fermionic systems. Please include with your complete application the contact details of three references.


[1] Non-abelian symmetries in tensor networks: A quantum symmetry space approach, A. Weichselbaum, Annals of Physics, 2012.

[2] Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet, Liu et al., PRB(R), 2015.