Hybrid molecular dynamics-quantum mechanics simulations of solute spectral properties in the condensed phase: evaluation of simulation parameters

We have explored the impact of a number of basic simulation parameters on the results of a recently developed hybrid molecular dynamics-quantum mechanics (MD-QM) method (Mercer et al., J Phys Chem B 1999, 103, 7720). The method utilizes MD simulations to explore the ground-state configuration space of the system and QM evaluation of those structures to yield the time-dependent electronic transition energy, which is transformed into the optical line-broadening function using the second-order cumulant expansion. Both linear and nonlinear optical spectra can then be generated for comparison to experiment. The dependence of the resulting spectra on the length of the MD trajectory, the QM sampling rate, and the QM model chemistry have all been examined. In particular, for the system of oxazine-4 in methanol studied here, at least 20 ps of MD trajectory are needed for qualitative convergence of linear spectral properties, and >100 ps is needed for quantitative convergence. Surprisingly, little difference is found between the 3-21G and 6-31G(d) basis sets, and the CIS and TD-B3LYP methods yield remarkably similar spectra. The semiempirical INDO/s method yields the most accurate results, reproducing the experimental Stokes shift to within 5% and the FWHM to within 20%. Nonlinear 3-pulse photon echo peak shift (3PEPS) decays have also been simulated. Decays are generally poorly reproduced, though the initial peak shift which depends on the overall coupling of motions to the solute transition energy is within 15% of experiment for all model chemistries other than those using the STO-3G basis.     

A practical introduction to tensor networks: Matrix product states and projected entangled pair states

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d$d$ and 2d$2d$ quantum lattice systems are also discussed.     

PEPS as ground states: Degeneracy and topology

We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries.