Regensburg 2022 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 21: Correlated Electrons: Poster Session
TT 21.10: Poster
Wednesday, September 7, 2022, 15:00–18:00, P1
Hierarchical equations of motion approach to open quantum dynamics: Matrix product state formulation in twin space — •Yaling ke1, Raffaele Borrelli2, and Michael Thoss1 — 1Institute of Physics, Albert-Ludwig University Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany — 2DISAFA, Università di Torino, I-10095 Grugliasco, Italy
The hierarchical equations of motion (HEOM) is a numerically exact approach to studying open quantum dynamics with strong non-perturbative and non-Markovian system-environment interactions at finite temperatures. Although considerable progress has been made over the past few decades to extend the applicability of the HEOM approach, the numerical cost is still very expensive for reasonably large systems.
In this contribution, we present the twin-space formulation of the HEOM approach in combination with the matrix product state representation for an open quantum system coupled to a hybrid fermionic and bosonic environment. The key ideas are a reformulation of a set of differential equations for the auxiliary density matrices into a time-dependent Schroedinger-like equation for an augmented multi-dimensional wave function as well as its tensor decomposition into a product of low-rank matrices. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems with both factorized and correlated initial condition.