# tdvp¶

Classes

 Engine(psi, model, TDVP_params[, environment]) Time dependant variational principle ‘Engine’. H0_mixed(Lp, Rp) Class defining the zero site Hamiltonian for Lanczos. H1_mixed(Lp, Rp, W) Class defining the one site Hamiltonian for Lanczos. H2_mixed(Lp, Rp, W0, W1) Class defining the two sites Hamiltonian for Lanczos.

Module description

Time Dependant Variational Principle (TDVP) with MPS (finite version only).

The TDVP MPS algorithm was first proposed by [Haegeman2011]. However the stability of the algorithm was later improved in [Haegeman2016], that we are following in this implementation. The general idea of the algorithm is to project the quantum time evolution in the manyfold of MPS with a given bond dimension. Compared to e.g. TEBD, the algorithm has several advantages: e.g. it conserves the unitarity of the time evolution and the energy (for the single-site version), and it is suitable for time evolution of Hamiltonian with arbitrary long range in the form of MPOs. We have implemented the one-site formulation which does not allow for growth of the bond dimension, and the two-site algorithm which does allow the bond dimension to grow - but requires truncation as in the TEBD case.

Todo

This is still a beta version, use with care. The interface might still change.

Todo

long-term: Much of the code is similar as in DMRG. To avoid too much duplicated code, we should have a general way to sweep through an MPS and updated one or two sites, used in both cases.