192 research outputs found
Path integrals in the physics of lattice polarons
A path-integral approach to lattice polarons is developed. The method is
based on exact analytical elimination of phonons and subsequent Monte Carlo
simulation of self-interacting fermions. The analytical basis of the method is
presented with emphasis on visualization of polaron effects, which path
integrals provide. Numerical results on the polaron energy, mass, spectrum and
density of states are given for short-range and long-range electron-phonon
interactions. It is shown that certain long-range interactions significantly
reduce the polaron mass, and anisotropic interactions enhance polaron
anisotropy. The isotope effect on the polaron mass and spectrum is discussed. A
path-integral approach to the Jahn-Teller polaron is developed. Extensions of
the method to lattice bipolarons and to more complex polaron models are
outlined.Comment: 40 pages, 12 figures, to be published in "Polarons in Advanced
Materials" ed. A.S. Alexandrov (Canopus Books, 2007
Light and stable triplet bipolarons on square and triangular lattices
We compute the properties of singlet and triplet bipolarons on
two-dimensional lattices using the continuous time quantum Monte Carlo
algorithm. Properties of the bipolaron including the total energy, inverse
mass, bipolaron radius and number of phonons associated with the bipolaron
demonstrate the qualitative difference between models of electron phonon
interaction with long-range interaction (screened Fr\"ohlich) and those with
purely local (Holstein) interaction. A major result of our survey of the
parameter space is the existence of extra-light hybrid singlet bipolarons
consisting of an on-site and an off-site component on both square and
triangular lattices. We also compute triplet properties of the bipolarons and
the pair dispersion. For pair momenta on the edge of the Brillouin zone of the
triangular lattice, we find that triplet states are more stable than singlets
Stability of three-fermion clusters with finite range of attraction
Three quantum particles with on-site repulsion and nearest-neighbour
attraction on a one-dimensional lattice are considered. The three-body
Schroedinger equation is reduced to a set of single-variable integral
equations. Energies of three-particle bound complexes (trions) are found from
self-consistency of the approximating matrix equation. In the case of spin-1/2
fermions, the ground state trion energy, the excited state energies, the trion
spectra and stability regions are obtained for total spins S = 1/2 and S = 3/2.
In the S = 1/2 sector, a narrow but finite parameter region is identified where
the ground state consists of a stable fermion pair and an unbound fermion. Also
presented is the reference case of spin-0 bosons.Comment: 6 pages, 5 figures, plus 3 pages of supplementary materia
Singlet and triplet bipolarons on the triangular lattice
We study the Coulomb-Fr\"ohlich model on a triangular lattice, looking in
particular at states with angular momentum. We examine a simplified model of
crab bipolarons with angular momentum by projecting onto the low energy
subspace of the Coulomb-Fr\"ohlich model with large phonon frequency. Such a
projection is consistent with large long-range electron-phonon coupling and
large repulsive Hubbard . Significant differences are found between the band
structure of singlet and triplet states: The triplet state (which has a flat
band) is found to be significantly heavier than the singlet state (which has
mass similar to the polaron). We test whether the heavier triplet states
persist to lower electron-phonon coupling using continuous time quantum Monte
Carlo (QMC) simulation. The triplet state is both heavier and larger,
demonstrating that the heavier mass is due to quantum interference effects on
the motion. We also find that retardation effects reduce the differences
between singlet and triplet states, since they reintroduce second order terms
in the hopping into the inverse effective mass.Comment: Proceedings of SNS 200
Isotope effect on the electron band structure of doped insulators
Applying a continuous-time quantum Monte-Carlo algorithm we calculate the
exact coherent band dispersion and the density of states of a two dimensional
lattice polaron in the region of parameters where any approximation might fail.
We find an isotope effect on the band structure, which is different for
different wave-vectors of the Brillouin zone and depends on the radius and
strength of the electron-phonon interaction. An isotope effect on the electron
spectral function is also discussed.Comment: 4 pages, 3 figure
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