Excited-State Geometry Optimization with the Density Matrix Renormalization Group, as Applied to Polyenes

Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians

A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.

Hückel-Hubbard-Ohno modeling of π-bonds in ethene and ethyne with application to trans-polyacetylene

Quantum chemistry calculations provide the potential energy between two carbon atoms in ethane (H3C-CH3), ethene (H2C[double bond, length as m-dash]CH2), and ethyne (HC[triple bond, length as m-dash]CH) as a function of the atomic distance. Based on the energy function for the σ-bond in ethane, Vσ(r), we use the Hückel model with Hubbard-Ohno interaction for the π electrons to describe the energies Vσπ(r) and Vσππ(r) for the σπ double bond in ethene and the σππ triple bond in ethyne, respectively. The fit of the force functions shows that the electron transfer matrix element and the Peierls coupling can be estimated with some precision whereas the Hubbard-Ohno parameters are insignificant at the distances under consideration. We apply the Hückel-Hubbard-Ohno model to describe the bond lengths and the energies of elementary electronic excitations of trans-polyacetylene, (CH)n, whereby we adjust the σ-bond potential for conjugated polymers.

Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics

Due to the crucial role played by electron correlation, the accurate determination of ground state geometries of π-conjugated molecules is still a challenge for many quantum chemistry methods. Because of the high parallelism of the algorithms and their explicit treatment of electron correlation effects, Quantum Monte Carlo calculations can offer an accurate and reliable description of the electronic states and of the geometries of such systems, competing with traditional quantum chemistry approaches. Here, we report the structural properties of polyacetylene chains H-(C₂H₂)(N)-H up to N = 12 acetylene units, by means of Variational Monte Carlo (VMC) calculations based on the multi-determinant Jastrow Antisymmetrized Geminal Power (JAGP) wave function. This compact ansatz can provide for such systems an accurate description of the dynamical electronic correlation as recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 2015 11 (2), 508-517]. The calculated Bond Length Alternation (BLA), namely the difference between the single and double carbon bonds, extrapolates, for N → ∞, to a value of 0.0910(7) Å, compatible with the experimental data. An accurate analysis was able to distinguish between the influence of the multi-determinantal AGP expansion and of the Jastrow factor on the geometrical properties of the fragments. Our size-extensive and self-interaction-free results provide new and accurate ab initio references for the structures of the ground state of polyenes.