Quantum Dynamics of Matrix Product States on Transformed bases

Hanggai Nuomin, Feng-Feng Song, David N. Beratan +1 more

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 multilevel 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 nonunitary 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 the bath. The transformation can be applied to quantum many-body systems, including spin chains and multilevel vibronic systems; the approach improves the numerical efficiency of the matrix product state simulations.

Kyu Hwang Yeon, Suk Seong Kim, Chung‐In Um +1 more

Sarah Croke, Stephen Mark Barnett, Stig Stenholm

Lei Wang, Jianing Zhuang, Xi Dai +1 more

We use the time dependent variational matrix product state (tVMPS) approach to investigate the dynamical properties of the single impurity Anderson model (SIAM). Under the Jordan-Wigner transformation, the SIAM is reformulated into two spin-1/2 XY chains with local magnetic fields along the z-axis. The chains are connected by the longitudinal Ising coupling at the end points. The ground state of the model is searched variationally within the space spanned by the matrix product state (MPS). The temporal Green's functions are calculated both by the imaginary and real time evolutions, from which the spectral information can be extracted. The possibility of using the tVMPS approach as an impurity solver for the dynamical mean field theory is also addressed. Finite temperature density operator is obtained by the ancilla approach. The results are compared to those from the Lanczos and the Hirsch-Fye quantum Monte-Carlo methods.

Vladimir S. Filinov

Nuomin, Hanggai, Feng-Feng Song, Peng Zhang +1 more

The possibility of using similarity transformations to alter dynamical entanglement growth in matrix-product-state simulations of quantum systems is explored. By appropriately choosing the similarity transformation, the entanglement growth rate is suppressed, improving the efficiency of numerical simulations of quantum systems. The transformation can be applied to general quantum-many-body systems.