E.Y. Loh

Correlations in a two band model of halogen-bridged transition metal linear chain complexes

Abstract We have studied the effects of correlations in a simple two-band discrete tight-binding Peierls-Hubbard model for MX chains using perturbation theory, Hartree-Fock and exact diagonalization for classical adiabatic phonons, and a variational approach for quantum phonons.

The extended Peierls-Hubbard model: Off-diagonal terms

Abstract We investigate the effects of including “off-diagonal” terms-nearest-neighbor bond-bond repulsion ( W ) and bond-site repulsion ( X ) — in the extended Peierls-Hubbard model. As a specific illustration we study the ground state dimerization in the one-dimensional, half-filled-band models that have been widely applied to conjugated polymers such as trans -polyacetylene and related charge density wave systems.

Optical absorption in extended Peierls-Hubbard models

Abstract We examine the optical absorption spectra for half-filled, one-dimensional systems involving both electron-phonon and electron-electron interactions as described by extended Peierls-Hubbard models. Exactly diagonalizing rings up to 12 sites, we examine the effects of electronic correlations in the intermediate- and strong-coupling regimes. In particular, using a novel “phase-randomization” technique, we are able to obtain absorption spectra with high resolution. Using a combination of weak- and strong-coupling and “decoupled dimer” analytic arguments, we are able to obtain a qualitative understanding of our numerical results over a wide range of electronic interactions and lattice distortions.

Extracting Infinite System Properties from Finite Size Clusters: 'Phase Randomization/Boundary Condition Averaging'

Abstract When electron-electron correlations are important, it is often necessary touse “exact” numerical methods, such as Lanczos diagonalization, to study the full many-body Hamiltonian. Unfortunately, such exact diagonalization methods are restricted to small system sizes. We show that if the Hubbard U term is replaced by a “periodic Hubbard” term, the full many body Hamiltonian may be exactly solved, even for very large systems, though for low fillings. However, for half-filled systems and large U this approach is not only no longer exact, it no longer improves extrapolation to larger systems. We discuss how generalized “randomized variable averaging” (RVA) or “phase randomization” schemes can be reliably employed to improve extrapolation to large system sizes in this regime. This general approach can be combined with any many-body method and is thus of broad interest and applicability.

Determination of interaction parameters in peierls-hubbard models describing finite polyenes and polyacetylene

Abstract We study the extent to which finite polyenes and polyacetylene can be described by the extended Peierls-Hubbard Hamiltonian (ePHH) in an internally consistent manner. Using Lanczos exact diagonalization methods (LEDM) on small systems, coupled with a novel boundary condition (b.c.) averaging technique, we investigate the excited state spectra of these models for the finite oligomer analogs of trans -polyacetylene, ( CH ) x . We search for sets of parameters describing the electron-phonon (e-p) and electron-electron (e-e) interactions which are consistent with all available experimental data on these systems, including the optical gap and bandwidth, the 2 1 A g state, longitudinal optical phonon frequency ω LO 2 , triplet excitations, and the optical absorptions assigned to charged and neutral solitons and to polarons. We conclude that the e-p coupling is substantially weaker than that suggested by purely e-p models and that the e-e interaction parameters are in the intermediate coupling regime ( U ∼ 2.5 t 0 ), consistent with values deduced from the finite polyenes.

MX chains: 1-D analog of CuD planes?

We study a two-band Peierls-Hubbard model for halogen-bridged mixed-valence transition metal linear chain complexes (MX chains). We include electron-electron correlations (both Hubbard and PPP-like expressions) using several techniques including calculations in the zero-hopping limit, exact diagonalization of small systems, mean field approximation, and a Gutzwiller-like Ansatz for quantum phonons. The adiabatic optical absorption and phonon spectra for both photo-excited and doping induced defects (kinks, polarons, bipolarons, and excitons) are discussed. A long period phase which occurs even at commensurate filling for certain parameter values may be related to twinning. The effect of including the electron-phonon in addition to the electron-electron interaction on the polaron/bipolaron (pairing) competition is especially interesting when this class of compounds is viewed as a 1-D analog of high-temperature superconductors. 6 refs., 4 figs.

Effects of electron-electron correlations and quantum phonons in a 3/4-filled, 2-band Peierls-Hubbard Hamiltonian for MX chains

Abstract We have studied the effects of electron-electron (e-e) correlations on the ground state and excitations of MX chains within a 3/4-filled two-band discrete Peierls-Hubbard model with on-site and inter-site electron-phonon (e-p) couplings. We have used theory, Hartree-Fock and exact diagonalization for classical adiabatic phonons, and a viriational approach allowing for finite phonon frequency (quantum phonons). We compare model predictions with experiments on MX chains.

Lanczos Diagonalizations of the 1-D Peierls-Hubbard Model

In contrast to the relative simplicity of independent electron theories, models describing interacting electrons are in general difficult to treat adequately. In their full complexity, many-electron problems involving N electronic orbitals -each of which can be empty, singly occupied with an electron of either spin, or doubly occupied — require the solution of Hamiltonian matrices of size roughly 4 N by 4 N . For a given problem, symmetries and selection rules (total spin, mirror plane or electron-hole symmetry, etc.) can be used to reduce the size of the matrix, but its growth with N will still be exponential. Often one attempts to avoid this difficulty by use of approximations involving effective single-particle methods — such as Hartree-Fock or Fermi liquid theory — which assume that the full problem can be treated in terms of self-consistent (or renormalized) nearly independent quasi-particle states. In Hartree-Fock, for example, one assumes that the full many-body wavefunction can be written as a single Slater determinant of one-particle wave functions. Accordingly, the problem for an N orbital system involves only an N by N matrix, albeit typically with self-consistency constraints on the parameters occurring in the Hamiltonian. Unfortunately, for strongly correlated systems such mean-field approaches can break down entirely; when the physical systems involve electronic motion in reduced dimensions, where strong quantum fluctuations can dominate the physics, this breakdown is particularly likely.

A Two Band Model for Halogen-Bridged Transition Metal Linear Chain Complexes

Halogen-bridged transition-metal complexes have been of interest to chemists for many decades as dyes and strongly dichroic materials [1]. However they have only recently begun to receive detailed consideration in the physics community [2–8]. Their potential importance arises because of: (i) The increasing appreciation of strong, competing electron-electron and electron-phonon interactions in low-dimensional materials and the consequent need to expand many-body techniques. The MX materials offer a rapidly expanding, near single-crystal (in contrast to, e.g., polyacetylene), class of quasi-1-D systems which can be “tuned” (by chemistry, pressure, doping, etc.) between various ground state extremes: from strong charge-disproportionation and large lattice distortion (e.g., ~ 20% distortion in PtCl) to weak charge-density-wave and small lattice distortion (e.g., ~ 5% distortion in PtI), to magnetic and undistorted (e.g., NiBr); (ii) The opportunity to probe doping- and photo-induced local defect states (polarons, bipolarons, kinks, excitons) and their interactions in controlled environments and the same large range of ground states; and (iii) The similarities between models and theoretical issues in these materials and the recently discovered oxide superconductors [3]. The MX materials are also closely connected conceptually with mixed-stack charge-transfer salts [9].