8 research outputs found
Numerical Study of a Two-Dimensional Quantum Antiferromagnet with Random Ferromagnetic Bonds
A Monte Carlo method for finite-temperature studies of the two-dimensional
quantum Heisenberg antiferromagnet with random ferromagnetic bonds is
presented. The scheme is based on an approximation which allows for an analytic
summation over the realizations of the randomness, thereby significantly
alleviating the ``sign problem'' for this frustrated spin system. The
approximation is shown to be very accurate for ferromagnetic bond
concentrations of up to ten percent. The effects of a low concentration of
ferromagnetic bonds on the antiferromagnetism are discussed.Comment: 11 pages + 5 postscript figures (included), Revtex 3.0, UCSBTH-94-2
Random Exchange Disorder in the Spin-1/2 XXZ Chain
The one-dimensional XXZ model is studied in the presence of disorder in the
Heisenberg Exchange Integral. Recent predictions obtained from renormalization
group calculations are investigated numerically using a Lanczos algorithm on
chains of up to 18 sites. It is found that in the presence of strong
X-Y-symmetric random exchange couplings, a ``random singlet'' phase with
quasi-long-range order in the spin-spin correlations persists. As the planar
anisotropy is varied, the full zero-temperature phase diagram is obtained and
compared with predictions of Doty and Fisher [Phys. Rev. B {\bf 45 }, 2167
(1992)].Comment: 9 pages + 8 plots appended, RevTex, FSU-SCRI-93-98 and
ORNL/CCIP/93/1
Pairing Correlations in a Generalized Hubbard Model for the Cuprates
Using numerical diagonalization of a 4x4 cluster, we calculate on-site s,
extended s and d pairing correlation functions (PCF) in an effective
generalized Hubbard model for the cuprates, with nearest-neighbor correlated
hopping and next nearest-neighbor hopping t'. The vertex contributions (VC) to
the PCF are significantly enhanced, relative to the t-t'-U model. The behavior
of the PCF and their VC, and signatures of anomalous flux quantization,
indicate superconductivity in the d-wave channel for moderate doping and in the
s-wave channel for high doping and small U.Comment: 5 pages, 5 figure
Effects of dimensionality and anisotropy on the Holstein polaron
We apply weak-coupling perturbation theory and strong-coupling perturbation
theory to the Holstein molecular crystal model in order to elucidate the
effects of anisotropy on polaron properties in D dimensions. The ground state
energy is considered as a primary criterion through which to study the effects
of anisotropy on the self-trapping transition, the self-trapping line
associated with this transition, and the adiabatic critical point. The effects
of dimensionality and anisotropy on electron-phonon correlations and polaronic
mass enhancement are studied, with particular attention given to the polaron
radius and the characteristics of quasi-1D and quasi-2D structures.
Perturbative results are confirmed by selected comparisons with variational
calculations and quantum Monte Carlo data
Triplet superconductivity in quasi one-dimensional systems
We study a Hubbard hamiltonian, including a quite general nearest-neighbor
interaction, parametrized by repulsion V, exchange interactions Jz, Jperp,
bond-charge interaction X and hopping of pairs W. The case of correlated
hopping, in which the hopping between nearest neighbors depends upon the
occupation of the two sites involved, is also described by the model for
sufficiently weak interactions. We study the model in one dimension with usual
continuum-limit field theory techniques, and determine the phase diagram. For
arbitrary filling, we find a very simple necessary condition for the existence
of dominant triplet superconducting correlations at large distance in the spin
SU(2) symmetric case: 4V+J<0. In the correlated hopping model, the three-body
interaction should be negative for positive V. We also compare the predictions
of this weak-coupling treatment with numerical exact results for the
correlated-hopping model obtained by diagonalizing small chains, and using
novel techniques to determine the opening of the spin gap.Comment: 8 pages, 3 figure
Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model
We present polaron effective masses and selected polaron band structures of
the Holstein molecular crystal model in 1-D as computed by the Global-Local
variational method over a wide range of parameters. These results are augmented
and supported by leading orders of both weak- and strong-coupling perturbation
theory. The description of the polaron effective mass and polaron band
distortion that emerges from this work is comprehensive, spanning weak,
intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly
adiabatic, and strongly adiabatic regimes. Using the effective mass as the
primary criterion, the self-trapping transition is precisely defined and
located. Using related band-shape criteria at the Brillouin zone edge, the
onset of band narrowing is also precisely defined and located. These two lines
divide the polaron parameter space into three regimes of distinct polaron
structure, essentially constituting a polaron phase diagram. Though the
self-trapping transition is thusly shown to be a broad and smooth phenomenon at
finite parameter values, consistency with notion of self-trapping as a critical
phenomenon in the adiabatic limit is demonstrated. Generalizations to higher
dimensions are considered, and resolutions of apparent conflicts with
well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure
Phase diagram of the Holstein polaron in one dimension
The behavior of the 1D Holstein polaron is described, with emphasis on
lattice coarsening effects, by distinguishing between adiabatic and
nonadiabatic contributions to the local correlations and dispersion properties.
The original and unifying systematization of the crossovers between the
different polaron behaviors, usually considered in the literature, is obtained
in terms of quantum to classical, weak coupling to strong coupling, adiabatic
to nonadiabatic, itinerant to self-trapped polarons and large to small
polarons. It is argued that the relationship between various aspects of polaron
states can be specified by five regimes: the weak-coupling regime, the regime
of large adiabatic polarons, the regime of small adiabatic polarons, the regime
of small nonadiabatic (Lang-Firsov) polarons, and the transitory regime of
small pinned polarons for which the adiabatic and nonadiabatic contributions
are inextricably mixed in the polaron dispersion properties. The crossovers
between these five regimes are positioned in the parameter space of the
Holstein Hamiltonian.Comment: 19 pages, 9 figure