David Luitz | CRC 1639 NuMeriQS

A06

Sat, 20 Jan 2024 17:07:25 +0100

Periodically driven quantum many-body systems are relevant for describing recent experiments in ultracold atom experiments and can be characterized by the structure of the eigenstates of the unitary generator of their dynamics. Accessing these states is a great computational challenge due to the exponential growth of the state space with system size and the dense structure of the generator. In this project, we will develop a high-performance technique for calculating exact eigenstates of such generators based on a complex polynomial transformation and the exploitation of symmetries of the system.

C02

Sat, 20 Jan 2024 17:07:25 +0100

The main goal of this project is to combine different methodologies effectively, leveraging their strengths against weaknesses. By integrating hybrid stochastic techniques with machine learning, multidimensional Tensor Networks, and the Iterative Configuration Expansion from quantum chemistry, our long term goal is to create a powerful approach to challenging quantum many-body systems. The objective is to unlock investigations of currently inaccessible quantum many-body systems at finite chemical potential, particularly focusing on QCD at finite baryon density and models for high-Tc superconductors.