Regensburg 2025 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Many-body Quantum Dynamics I (joint session DY/TT)

DY 13.5: Vortrag

Dienstag, 18. März 2025, 10:30–10:45, H37

Semigroup Influence Functionals for the Dynamics of Quantum Impurity Models — •Michael Sonner¹, Valentin Link², and Dmitry Abanin^3,4 — ¹Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany — ²Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany — ³Department of Physics, Princeton University, Princeton, New Jersey 08544, USA — ⁴Google Research, Brandschenkestrasse 150, 8002 Zürich, Switzerland

Quantum impurity models~(QIM) consist of a local interacting impurity which is coupled to baths of free fermions. These models exhibit a range of non-trivial phenomena such as the Kondo effect. and play a central role in the dynamic mean field theory (DMFT) approach to correlated matter. However, despite their importance, computing the real time dynamics of QIM remains a challenge. Recently, approaches based on matrix product states (MPS) representation of influence functionals (IF) have been proven effective approaches to this problem. These method work by capturing the, generically non-markovian dynamical effects of the quantum environments on the local impurity in a multi time object, which then is compressed as MPS. Taking explicit advantage of time-translation invariance of the model, we find an infinite MPS or semigroup representation of the IF. I will demonstrate how these ideas can be used to predict QIM dynamics for very long times as well as give direct access to stationary non-equilibrium states.

Keywords: Anderson impurity model; Non-equilibrium physics; Quantum Impurity Problems; Tensor Network methods; Open Quantum Systems