# P2: Realistic spin models for strongly correlated materials

## Project Description

Strongly-correlated spin systems are often described through Heisenberg-like spin-models with parameters obtained from density-functional theory (DFT)-based calculations, e.g., in the LDA+*U* approximation. This approach relies on the assumption that the correlation effects relevant for the magnetic exchange couplings are sufficiently well described via the Hartree-Fock approximation which is at the core of the LDA+*U* approach, although it is well known that the magnetic spectrum is not. An alternative approach consists of starting from material-specific Hubbard models. To obtain the magnetic couplings of the low-energy spin Hamiltonian one can either integrate out charge fluctuations via canonical transformations^{(1),(2)}, or extract them from the solution of the Hubbard model, e.g. obtained via dynamical mean-field theory (DMFT) or its cluster extensions (CDMFT). In the latter case, two approaches are possible: extract the exchange couplings by comparing the total energy of different spin configurations or calculate them using a local force theorem^{(3)}.

In this project, we plan to systematically test the regime of validity of these three approaches (canonical transformation, spin configurations, and local force theorem) for representative strongly correlated materials. First, we will construct material-specific Hubbard models using Wannier functions. Next we will solve these models in the paramagnetic regime by means of the LDA+*U* (Hartree-Fock) as well as the dynamical mean-field theory or its

cluster extensions (LDA+DMFT approach)^{(4)}. Finally, we will construct the low energy spin Hamiltonians via the three approaches discussed above.

In the last part of the project, we will calculate the magnetic structure of the system with DMFT ^{(4)} starting from the Hubbard model and compare the results with those obtained solving directly the spin-Hamiltonian with Monte Carlo

techniques^{(5)-(13)}. We will consider first magnetic correlated systems for which we already performed extensive electronic-structure and/or LDA+DMFT studies in the paramagnetic region: the series of one-band two-dimensional frustrated systems^{(14),(15)} and two-band strongly-correlated orbitally-ordered materials (rare-earth manganites and cuprates)^{(16),(17)}. For the DMFT calculations we will use a general implementation, which we have recently developed^{(18)}, based on the strong coupling continuous time quantum Monte Carlo method.

The final aim is to establish the optimal scheme for deriving spin models for strongly correlated systems.

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E. Pavarini, E. Koch, A. Lichtenstein and D. Vollhardt (eds.), Verlag des Forschungszentrum Jülich, 2011

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(18) A. Flesch, E. Gorelov, E. Koch and E. Pavarini, Phys. Rev. B **87**, 195141 (2013)