Matrix product state formulation of the multiconfiguration time-dependent Hartree theory

Abstract: A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized in the MCTDH ansatz and thus results in an exponential increase of the computational cost, is parametrized by the MPS form. Equations of motion based on the Dirac-Frenkel time-dependent variational principle is derived by using the tangent space projection and the projector-splitting technique for the MPS, which have been recently developed. The mean-field operators, which appears in the equation of motion of the MCTDH single particle functions, are written in terms of the MPS form and efficiently evaluated by a sweep algorithm that is similar to the DMRG sweep. The efficiency and convergence of the MPS formulation to the MCTDH are demonstrated by quantum dynamics simulations of extended excitonic molecular systems.