Suppressing the entanglement growth in matrix product state evolution of quantum systems through nonunitary similarity transformations

Abstract

In strong-coupling regimes, quantum dynamical effects can alter conventional physics described by perturbation theories, but the dynamical simulations of these quantum systems using matrix product states-such as multi-level vibronic systems that are relevant to energy and electron transfer reactions-suffer from rapid entanglement growth during their real-time evolution, impeding explorations of spectra, dynamics, and kinetics. We examine the possibility of using non-unitary transformations to alter dynamical entanglement growth in matrix-product-state simulations of quantum systems, using the spin-Boson model to showcase the reduced entanglement. By appropriately choosing the transformation, the entanglement growth rate is suppressed, improving the efficiency of quantum dynamical simulations. Entanglement control is achieved by the transformation-induced biased transitions among the system quantum states, and by "projecting" (approximately) the system quantum state to one of the eigenstates of the system-bath coupling operator, thus controlling the energy exchange between the system and bath. The transformation can be applied to quantum many-body systems, including spin chains and multi-level vibronic systems; the approach improves the numerical efficiency of the MPS simulations.