We adapted the Global Subspace Expansion (GSE) algorithm on tree tensor networks (TTN),integrated it into the Time Dependent Variational Principle algorithm (GSE-TDVP), to miti-gate the 1-site TDVP projection error, while achieving the accuracy of 2-site TDVP. We utilizedan adaptive adjustment of a truncation parameter within the GSE algorithm, to achieve stablebond growth under controlled conditions during the evolution. Furthermore, we investigatedthe representation of wave-function of 2D systems with spanning tree as an intermediate ap-proach between Matrix Product States (MPS) and Projected Entangled-Pair Sates (PEPS). Weconducted a methodological error analysis of the GSE-TDVP algorithm across various span-ning tree structures, and proposed a scoring metric based on TDVP performance and thenetwork connectivity. A significant bottleneck in the algorithm—matrix exponential approxi-mation—was addressed by incorporating an enhanced Krylov subspace projection method withadaptive time-stepping. Finally, we enhanced the Tensor Jump Method (TJM) by utilizingGSE-TDVP on spanning tree and benchmarked a simple dissipative dynamics on a 2D lattice.     «

We adapted the Global Subspace Expansion (GSE) algorithm on tree tensor networks (TTN),integrated it into the Time Dependent Variational Principle algorithm (GSE-TDVP), to miti-gate the 1-site TDVP projection error, while achieving the accuracy of 2-site TDVP. We utilizedan adaptive adjustment of a truncation parameter within the GSE algorithm, to achieve stablebond growth under controlled conditions during the evolution. Furthermore, we investigatedthe representation of wave-function of 2D syst...     »