Speaker
Description
Susceptibilities and optical conductivity are examples of two-particle response functions that are the key quantities for connecting theoretical predictions for correlated materials with experimental results. It can however become highly nontrivial to calculate them, especially in cases when nonlocal electronic correlations are important.
In my talk I will present a new computational approach to diagrammatic two-particle methods, namely the quantics tensor train representation [1], on the example of a set of self-consistent equations for two-particle vertex functions: the parquet equations. I will show that the steps needed to evaluate the equations (Bethe–Salpeter equations, parquet equation and Schwinger–Dyson equation) can be decomposed into basic operations on tensor trains. The repeated application of these operations does not lead to a loss of accuracy beyond a specified tolerance and the iterative scheme converges even for numerically demanding parameters. The applied methods allow for an exponential increase of the number of grid points included in the calculations, and a corresponding exponential reduction of the computational error, for a linear increase in computational cost [2].
[1] Phys. Rev. X 13, 021015 (2023)
[2] Phys. Rev. Research 7, 023087 (2025)