DMFT-QE Symposium: April 14th

Talk 1:

Towards an ab initio theory for high-temperature superconductors

Benjamin Bacq-Labreuil, Institut de Physique et Chimie des Matériaux de Strasbourg

Significant progress towards a theory of high-temperature superconductivity in copper-oxide materials (cuprates) has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions remain challenging due to the complex relationship between real materials and the effective models. In this presentation, we will show that the goal of material-specific predictions for high-temperature superconductors from first principles is within reach, by exploiting a combination of density functional theory and cluster dynamical mean-field theory. We take on the challenge of explaining the remarkable physics of multilayer cuprates, such as their universal dependence of superconductivity on the number of consecutive copper-oxide planes, the link with the inhomogeneous doping between different CuO2 planes and how this translates into co-existence of arcs and pockets in the Fermi surface. We shall motivate that our contribution establishes a framework for comprehensive studies of cuprates, and open perspectives for theoretical material design of high-temperature superconductors.

Talk 2:

Compact sum-of-exponentials representations of imaginary time functions, and an application to Feynman diagram evaluation

Jason Kaye, Flatiron Institute

Several systematic and high precision methods for generating compact sum-of-exponentials (SOE) expansions of imaginary time quantities have been introduced in the past several years, including the intermediate representation, the discrete Lehmann representation, the AAA algorithm, Prony’s method, and ESPRIT. I will briefly discuss some of these, and describe an application to the fast and deterministic evaluation of imaginary time Feynman diagrams of low-to-intermediate order, in particular those arising from the bold hybridization expansion of the Anderson impurity model. The central idea is to use an SOE expansion of the hybridization function to separate variables, decomposing the multiple integrals into sequences of nested convolutions, which can again be computed efficiently using imaginary time compression techniques. This leads to a fast “approximate” impurity solver for dynamical mean-field theory which is deterministic, and offers favorable scaling at low temperatures and user-controlled accuracy at a fixed expansion order.

[1] Z. Huang, D. Golež, H. U. R. Strand, J. Kaye, “Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting”, arXiv:2503.19727 (2025).
[2] J. Kaye, Z. Huang, H. U. R. Strand, D. Golež, “Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion”, Phys. Rev. X, 14, 031034 (2024).