NCTS Taiwan

Feynman diagrams form a formal solution to the many-body problem. They transform an exponentially large problem (e.g. finding the lowest eigenstate of an exponentially large matrix) into another exponentially difficult problem (calculating an exponential number of diagrams). In this seminar, I will discuss our journey to automatise these calculations in the context of quantum nanoelectronics.
I will show in particular our latest technique that uses tensor trains to calculate the diagrams. With this technique, we have been able to calculate all Feynman diagrams up to order 30 for an out-of-equilibrium single impurity Anderson model. I will show the physics that emerges from these data, in particular the formation of the Kondo cloud after a quench and the formation of the Kondo ridge in the the current voltage characteristics.

We design a protocol that  design concurrently a frustration-free quantum many-body Hamiltonian and its exact ground states in one and two dimensions using MPS.
It was shown previously that for any given translationally invariant injective MPS, there always exists a parent Hamiltonian which is gapped and frustration free. However, our way of dealing with the problem expands the applicability to wider classes of models, providing a systematic way of constructing a series of exact solutions in the MPS representation for any given frustration-free model at finite system size.
We show the application to 1D frustrated spin chains, Toric codes, triangular and kagome lattices where we find an exact topologically nontrivial or gapless multicritical point solutions.