Theoretical Solid State Physics

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Real-frequency dynamical mean field theory treatment of correlated multi-band lattice models

Real-frequency dynamical mean field theory treatment of correlated multi-band lattice models

A major long-term challenge in condensed matter theory is the development of reliable computational tools for  quantitative materials research -- the ultimate goal being to start from ab initio methods for computing band structure  properties, while accurately accounting for correlation effects induced by interactions.

A widely-used method for dealing with interactions in strongly-correlated electron systems and electronic structure calculations is dynamical mean-field theory (DMFT) [1,2]. It treats the interplay between a given lattice site (the “impurity”) and the rest of the lattice (the “bath”) as a quantum impurity model with a self-consistently determined hybridization function. Since DMFT’s performance depends on that of the method used to solve this impurity model, much effort has been invested over the years to develop ever more powerful impurity solvers. For multi-band models, continuous-time quantum Monte Carlo (CTQMC) methods have long been the leading impurity solvers in terms of versatility and performance [3]. However, they are not without limitations: sign problems can occur, low-temperature calculations are costly, and obtaining real-frequency spectra requires analytic continuation of imaginary (Matsubara) frequency QMC data, which is notoriously difficult. Thus, there is a continued need for real frequency impurity solvers suitable for multi-band DMFT applications.

We have recently demonstrated that the numerical renormalization group (NRG) is a viable multi-band impurity solver for DMFT, offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures [4]. Using DMG+NRG, we were able to clarify several open questions regarding a minimal model of a three-band “Hund metal” (relevant for studies of iron pnictide superconductors), which has both a Hubbard interaction U and a  ferromagnetic Hund coupling J. Moreover, this project demonstrated that having access to real-frequency information is truly valuable for understanding the relevant physical processes at various different energy scales.

I am currently looking for a PhD student to continue this very promising line of research. Our next step will be to study more realistic multi-band models, involving less orbital symmetry or including spin-orbit interactions. Though such  models are more challenging than that studied in [4], their treatment should be feasible using several recent  refinements in NRG methodology developed by our group [5-7]. In the medium term, we will aim to integrate our DMFT+NRG tools with ab initio band structure methods to calculate ac and dc transport properties in strongly correlated materials, such as high-temperature superconductors, iron pnictides, chalcogenides, ruthenates and other 4d transition metal oxides.

Suitable candidates should  have a good understanding of many-body physics and enjoy doing numerical work and method development.

[1] A. Georges, G. Kotliar, W. Krauth and M. J. Rozenberg
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
Rev. Mod. Phys. 68, 13 (1996).

[2] G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet and C. A. Marianetti
Electronic structure calculations with dynamical mean-field theory
Rev. Mod. Phys. 78, 865-951 (2006).

[3] E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer and P. Werner
Continuous-time Monte~Carlo methods for quantum impurity models
Rev. Mod. Phys. 83, 349-404 (2011).

[4] K. M. Stadler, Z. P. Yin, J. von Delft, G. Kotliar and A. Weichselbaum
Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal
Phys. Rev. Lett. 115, 136401 (2015).

[5] K. M. Stadler, A. K. Mitchell, J. von Delft and A. Weichselbaum
Interleaved numerical renormalization group as an efficient multiband impurity solver Phys. Rev. B 93, 235101 (2016).

[6] S.-S. B. Lee and A. Weichselbaum
Adaptive broadening to improve spectral resolution in the numerical renormalization group
Phys. Rev. B 94, 235127 (2016).

[7] B. Bruognolo, N.-O. Linden, F. Schwarz, S.-S. B. Lee, K. Stadler, A. Weichselbaum, M. Vojta, F. B. Anders and J. von Delft
Open Wilson chains for quantum impurity models: Keeping track of all bath modes
arXiv:1611.05291 [cond-mat.str-el] (2016).