UC Irvine

We study one dimensional models of diatomic molecules where both the electrons and nuclei are treated as quantum particles, going beyond the usual Born-Oppenheimer approximation. The continuous system is approximated by a grid which computationally resembles a ladder, with the electrons living on one leg and the nuclei on the other. To simulate DMRG efficiently with this system, a three-site algorithm has been implemented. We also use a compression method to treat the long-range interactions between charged particles. We find that 1D diatomic molecules with spin-1/2 nuclei in the spin-triplet state will unbind when the mass of the nuclei reduces to only a few times larger than the electron mass, while the molecule with nuclei in the singlet state always binds, given the two electrons in their singlet state in both cases. We propose an improved scheme to do the time dependent variational principle (TDVP) in finite matrix product states (MPS) for two-dimensional systems or one-dimensional systems with long range interactions. We present a method to represent the time-evolving state in a MPS with its basis enriched by state-averaging with global Krylov vectors. We show that the projection error is significantly reduced so that precise time evolution can still be obtained even if a larger time step is used. Combined with the one-site TDVP, our approach provides a way to dynamically increase the bond dimension while still preserving unitarity for real time evolution. Our method can be more accurate and exhibit slower bond dimension growth than the conventional two-site TDVP. We apply our improved TDVP method to investigate the spin squeezing dynamics of the XXZ model of $1/r^\alpha$ interaction in two dimension. Comparing with the spin squeezing parameter and other observables obtained from discrete truncated Wigner approximation (DTWA), we verify the validity of DTWA and unveil the potential for this method to study dynamics of large-scale spin systems. Our results confirm the existence of large collective regime when $\alpha > 2$, which can be a guide for future experimental realizations. Combined with the purification method, our improved TDVP method is proved to be also useful to study the thermalization of the long-range interacting system.