pyTTN: An Open Source Toolbox for Open and Closed System Quantum Dynamics Simulations Using Tree Tensor Networks

We present the Python Tree Tensor Network package (pyTTN) for the evaluation of dynamical properties of closed and open quantum systems that makes use of Tree Tensor Network (TTN), or equivalently the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH), based representations of wavefunctions. This package includes several features allowing for easy setup of zero- and finite-temperature calculations for general Hamiltonians using single and multi-set TTN ans\"atze with an adaptive bond dimension through the use of subspace expansion techniques. All core features are implemented in C++ with Python bindings provided to simplify the use of this package. In addition to these core features, pyTTN provides several tools for setting up efficient simulation of open quantum system dynamics, including the use of the TTN ansatz to represent the auxiliary density operator space for the simulation of the Hierarchical Equation of Motion (HEOM) method and generalised pseudomode methods; furthermore we demonstrate that the two approaches are equivalent up to a non-unitary normal mode transformation acting on the pseudomode degrees of freedom. We present a set of applications of the package, starting with the widely used benchmark case of the photo-excitation dynamics of 24 mode pyrazine, following which we consider a more challenging model describing the exciton dynamics at the interface of a $n$-oligothiophene donor-C$_{60}$ fullerene acceptor system. Finally, we consider applications to open quantum systems, including the spin-boson model, a set of extended dissipative spin models, and an Anderson impurity model. By combining ease of use, an efficient implementation, as well as an extendable design allowing for the addition of future extensions, pyTTN can be integrated in a wide range of computational modelling software.