P1: Magnetic and orbital excitations in strongly-correlated materials

 

Project Description

To date, the realistic description of magnetic and orbital excitations in strongly-correlated materials remains challenging. A major step forward was reached via the DFT+DMFT technique [1], which is the state-of-the-art method for strongly-correlated systems. This technique combines ab-initio approaches based on density-functional-theory (DFT) with the many-body dynamical mean-field theory (DMFT). In standard DFT+DMFT calculations, material-specific Hubbard-like models are built using localized Wannier functions. These models are then solved via DMFT using a numerically exact quantum impurity solver, typically quantum Monte Carlo (QMC). This yields the local single-particle Green function matrix. In order to obtain magnetic and orbital excitations, it is necessary, however, to calculate the local dynamical two-particle Green function [2]. The lattice susceptibility can then be obtained by solving the Bethe-Salpeter equation in the so-called local-vertex approximation. This combination of methods has proved to be very successful, but the calculation of dynamical two-particle quantities is numerically very challenging for realistic Hamiltonians.

In this project we plan to establish an efficient DFT+DMFT-based scheme to calculate magnetic and orbital excitations for multi-orbital systems of any symmetry in a truly realistic setting and at experimental temperatures. To achieve this goal, we will employ the generalized continuous-time quantum Monte Carlo (CT-QMC) quantum-impurity solver as described in Refs. [3,4,5]. In the first funding period of the RTG, we already implemented a CT-QMC scheme for the calculations of generalized two-particle Green functions for general multi-orbital systems. Our current implementation, based on Legendre polynomial expansions, exploits the power of modern massively-parallel supercomputers. This allows us (i) to systematically build material-specific super-exchange models from static two-particle Green functions without any a-priori assumption on their form and (ii) to calculate the corresponding dynamical response functions. The calculation of dynamical quantities remains, however, numerically difficult as compared to static ones. This sets limits to the possibilities of studying low-energy magnetic and orbital excitations on a regular basis down to experimental temperatures. In order to overcome these problems, it is essential to discover possible alternative strategies. We have already shown that specific choices of the local basis can both tame the sign problem and reduce the computational time for the calculation of single-particle Green functions [6]. This idea has recently enabled us to study, for the first time, spin-orbit effects in ruthenates without approximations [3]. As a first step in the present pro-ject, we plan to expand on this to systematically explore similar strategies targeted to two-particle quantities. In particular, we plan to optimize the choice of (i) the analytical polynomial expansion, (ii) the basis for the QMC calculation, and (iii) the high-frequency extrapolation procedure. As a second step, we will implement a calculation scheme for magnetic and or-bital excitation spectra including form factors. We will compare DFT+DMFT results with those obtained from approximate analytical methods, such as classical spin-wave theory. We plan to compare results from Monte Carlo simulations [7,8,9,10,11] of the material-specific spin- (or pseudospin-) Hamiltonians which were constructed using static susceptibility calculations. As test cases we will initially study materials for which we have already performed extensive electronic-structure and/or DFT+DMFT studies, i.e. rare-earth manganites and orbitally-ordered cuprates [12,13].

[1] E. Pavarini, “The LDA+DMFT approach”, in The LDA+DMFT approach to strongly correlated materials, E. Pavarini, E. Koch, D. Vollhardt, and A. Lichtenstein (eds.), Modeling and Simulation Vol. 1, Verlag des Forschungszentrum Jülich (2011)
[2] E. Pavarini, “Linear response functions”, in DMFT at 25: Infinite Dimensions, Modeling and Simulation, E. Pavarini, E. Koch, D. Vollhardt, and A. Lichtenstein (eds.), Modeling and Simulation Vol. 4, Verlag des Forschungszentrum Jülich (2014)
[3] A. Flesch, E. Gorelov, E. Koch, and E. Pavarini, Phys. Rev. B 87, 195141 (2013)
[4] G. R. Zhang, E. Gorelov, E. Sarvestani, and E. Pavarini, Phys. Rev. Lett. 116, 106402 (2016)
[5] E. Sarvestani, G. R. Zhang, E. Gorelov, and E. Pavarini, Phys. Rev. B 97, 085141 (2018)
[6] E. Pavarini, “Linear response functions”, in DMFT at 25: Infinite Dimensions, Modeling and Simulation, E. Pavarini, E. Koch, D. Vollhardt, and A. Lichtenstein (eds.), Modeling and Simulation Vol. 4, Verlag des Forschungszentrum Jülich (2014)
[7] M. Lohöfer, T. Coletta, D. G. Joshi, F. F. Assad, M. Vojta, S. Wessel, and F. Mila, Phys. Rev. B 92, 245137 (2015)
[8] A. Honecker, S. Wessel, R. Kerkdyk, T. Pruschke, F. Mila, and B. Normand, Phys. Rev. B 93, 054408 (2016)
[9] M. Lohöfer and S. Wessel, Phys. Rev. Lett. 118, 147206 (2017)
[10] S. Wessel, B. Normand, F. Mila, and A. Honecker, SciPost Phys. 3, 005 (2017)
[11] J. Becker, T. Köhler, A. C. Tiegel, S. R. Manmana, and S. Wessel, Phys. Rev. B 96, 060403 (R) (2017)
[12] E. Pavarini and E. Koch, Phys. Rev. Lett. 104, 086402 (2010)
[13] E. Pavarini, E. Koch, and A.I. Lichtenstein, Phys. Rev. Lett. 101, 266405 (2008)