Time-dependent variational principle with ancillary Krylov subspace

Symmetric cluster expansions with tensor networks

“…While this method is competitive with other time-evolution schemes, we believe it is best used in tandem with the TDVP: using the TDVP for the main time evolution, and the cluster expansion MPO to increase the bond dimension. Increasing bond dimension such that spatial symmetries are conserved is nontrivial yet crucial for accurate simulation [16,17], and with a cluster MPO time step one can do just that. Additionally, a large time step allows for a more accurate bond dimension increase than several bond increases with small time steps, as must be done in most time-evolution schemes.…”

Studying dynamics in two-dimensional quantum lattices using tree tensor network states

“…While the TDVP applied to MPS has been demonstrated to be capable of simulating dynamics in two-dimensional systems [21], a detailed analysis and comparison with other tensor network structures is absent in the literature. In particular, the numerical stability of the TDVP cannot be taken for granted [68], especially when interactions between sites are long-ranged and not…”

“…However, this scheme requires the evaluation of an effective Hamiltonian matrices forĤ 2 and its compatibility with the integration scheme employed here is an open question. Recently, another approach based on a global basis expansion for MPS has been presented, and should also be applicable to general TTNS [68].…”

Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states

“…That there is a need for an MPS time evolution algorithm that retains the desirable properties of the 1TDVP, while allowing bond dimensions to change in response to emerging entanglement, is widely agreed upon in the literature and there have recently been a number of papers which make progress in this direction 10,15,59,62 . Notably, Yang and White 62 have proposed a general, bond-adaptive 1TDVP variant, drawing on ideas related to subspace expansions for one-site DMRG 29 , wherein the MPS is enriched at each step with the help of global Krylov vectors, which are constructed by several applications of the Hamiltonian's MPO to the MPS.…”

“…While conceptually different from the unoptimized expansion approach that we shall develop in this article, the global subspace expansion TDVP (GSE-TDVP) of Ref. 62 allows bond dimensions to grow during time-evolution with numerical costs and speeds that are intermediate between standard, fixed-D 1TDVP and 2TDVP. Moreover, GSE-TDVP is also able to handle certain classes of long-range problems for which both 1TDVP and 2TDVP will fail.…”