Regensburg 2022 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 16: Correlated Electrons: Method Development
TT 16.9: Vortrag
Mittwoch, 7. September 2022, 12:00–12:15, H10
Hierarchical equations of motion approach to open quantum system 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) approach is a numerically exact method to study the dynamics of open quantum systems with non-perturbative system-environment interaction and non-Markovian memory 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 open quantum systems coupled to a hybrid fermionic and bosonic environment. The key ideas of the approach are a reformulation of a set of differential equations for the auxiliary density matrices into a time-dependent Schrödinger-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 conditions.