One of the biggest challenges in the study of quantum many-body systems is the so-called “course of dimensionality”, namely, the exponential scaling of the system degrees of freedom with its size. Tensor networks have emerged as a general data compression scheme which, in the quantum mechanical context, enable the efficient truncation of the Hilbert space, by exploiting the intrinsic entanglement structure of quantum states.<br/><br/>Using a tensor network approach, we propose a mechanism for the controlled time-evolution of the nuclear degrees of freedom of multi-configurational chemical systems at a reduced storage and computational complexity. The procedure is rooted in the matrix product decompositions of both, the Trotterized unitary time-evolution operator and the nuclear wave function. In order to preserve the compression advantage gained by tensor network decompositions, the potentially exponential growth of non-physical entanglement degrees of freedom at each time-step, must be suppressed. We present an efficient algorithm for the regularization of such entanglement dimensions, which is applicable to any quantum dynamical problem, but particularly useful for dynamical simulations of nuclear chemical systems.<br/><br/>Our algorithm is probed using a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine. This system is chosen for its simplicity which enables direct diagonalization calculations; therefore, providing an excellent comparison tool for the accuracy of our method.

Entanglement regularization in quantum dynamics of tensor network states

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