Abstracts – Group seminar

Numerical Methods for imaginary and real-time Green’s functions

Hugo U.R. Strand

Describing the real-time dynamics of interacting quantum many-body systems is a formidable challenge. Green’s function based methods can be readily extended to real-time dynamics by using the Kadanoff-Baym real-time contour Green’s function formalism [1], where the components of the Green’s function acquire two independent time arguments.

Numerical simulations require some form of discretization of the time dependence, and straight forward equidistant time grid has been successfully used for small model systems [2]. For a given discretization, the second challenge is to develop robust and accurate numerical algorithms for solving the Dyson equation of motion for the Green’s function.

In this talk I will present progress on both these aspects. The discrete Lehmann representation (DLR) [3] is a new discretization scheme for the imaginary time branch with asymptotic optimal scaling and analytic basis functions. The DLR has logarithmic scaling of the number of discretization points with respect to the inverse temperature, a drastic improvement compared to the equidistant grid exhibiting linear scaling.

By combining the DLR with an equidistant real-time grid we have developed a fast equilibrium real-time solver for the Dyson equation [4], where the real-time history integral is evaluated using FFT, enabled by a hierarchical decomposition of the convolution matrix. This enables the study of both low temperature and low energy phenomena like the low frequency square root divergence in the Sachdev-Yitaev-Ke model.

[1] G. Stefanucci and R. van Leeuwen,
Nonequilibrium Many-Body Theory of Quantum Systems A Modern Introduction,
Cambridge University Press (2013)
[2] M. Schüler, et al., Comput. Phys. Commun., v257, 107484 (2020)
[3] J. Kaye, et al., arXiv:2107.13094, J. Kaye, HURS, arXiv:2110.06765

[4] J. Kaye, HURS, arXiv:2110.06120

Ab initio QED: Combining strong light-matter interaction with realistic materials and its application to chemistry

Christian Schäfer

The alchemical dream of altering a given material on demand into something desirable is at the very heart of chemistry.
Cavity environments provide a novel handle to non-intrusively control materials and chemistry as demonstrated by recent experimental work. A theoretical description of those systems is challenging, to put it mildly. The self-consistent interaction between complex electromagnetic environments and realistic materials gave birth to a new discipline, sometimes referred to as ’ab initio QED’, on the interface of condensed matter and quantum optics.

I will provide an introduction into this newly emerged field, discuss important conditions [1], highlight its strength, current limitations and future prospects. In a first step, a non-perturbative photon-free framework [2] will be introduced that provides access to strong and even deep ultra-strong-coupling phenomena by expressing quantum fluctuations of the field as fluctuations of the currents. Subsequently, the left over classical Maxwell fields can be efficiently embedded into state-of-the-art ab initio libraries [3]. From this perspective, the current state of ab initio QED will be briefly reviewed. Finally, I will present applications to chemistry, demonstrating modifications in weak intermolecular interactions [4] and the speed of chemical reactions [5] by means of an external cavity.

Contact e-mails:
christian.schaefer.physics@gmail.com

[1] Christian Schäfer, Michael Ruggenthaler, Vasil Rokaj, and Angel Rubio, ACS Photonics 2020 7 (4), 975, doi: 10.1021/acsphotonics.9b01649.

[2] Christian Schäfer, Florian Buchholz, Markus Penz, Michael Ruggenthaler, and Angel Rubio, PNAS 2021 Vol. 118 No. 41 e2110464118, doi: 10.1073/pnas.2110464118.

[3] Christian Schäfer and Göran Johansson, http://arxiv.org/abs/2106.07507, (2021).

[4] Tor S. Haugland, Christian Schäfer, Enrico Ronca, Angel Rubio, and Henrik Koch, J. Chem. Phys. 154, 094113 (2021); doi: 10.1063/5.0039256.

[5] Schäfer, C., Flick, J., Ronca, E., Narang, P., and Rubio, A., arXiv:2104.12429 (2021).

Phenomenology of transport in semiconductors & Resistivity saturation in Kondo insulators

Jan M. Tomczak

We devise a methodology for charge, heat, and entropy transport driven by carriers with finite lifetimes.Combining numerical simulations with analytical expressions for low temperatures, we establish a comprehensive and thermodynamically consistent phenomenology for transport properties in semiconductors [1]. As an example, we consider heavy-fermion insulators: Their resistivity typically saturates below a characteristic temperature T*. In our scenario [2], finite lifetimes of intrinsic carriers drive residual conduction, impose the existence of a crossover T*, and control – on par with the charge gap – the quantum regime emerging below. We showcase this mechanism for the Kondo insulator Ce3Bi4Pt3, for which residual conduction is a bulk property, and elucidate how its saturation regime evolves under external pressure and varying disorder. Deriving a phenomenological formula for the quantum regime, we also unriddle the ill-understood bulk conductivity of

SmB6 – demonstrating a wide applicability of our mechanism in correlated narrow-gap semiconductors [3]. Finally, we extend the discussion to signatures of finite electronic lifetimes in the coefficients of Hall, Seebeck and Nernst.

[1] M. Pickem, E. Maggio, J.M. Tomczak, (in preparation, 2021)

[2] M. Pickem, E. Maggio, J.M. Tomczak, Commun. Phys 4, 226 (2021)

[3] J.M. Tomczak, J. Phys.: Condens. Matter 30, 183001 (2018)