49 research outputs found
Diffusion and localization of relative strategy scores in the Minority Game
We study the equilibrium distribution of relative strategy scores of agents
in the asymmetric phase () of the basic Minority
Game using sign-payoff, with agents holding two strategies over
histories. We formulate a statistical model that makes use of the gauge freedom
with respect to the ordering of an agent's strategies to quantify the
correlation between the attendance and the distribution of strategies. The
relative score of the two strategies of an agent is described
in terms of a one dimensional random walk with asymmetric jump probabilities,
leading either to a static and asymmetric exponential distribution centered at
for fickle agents or to diffusion with a positive or negative drift for
frozen agents. In terms of scaled coordinates and the
distributions are uniquely given by and in quantitative agreement with
direct simulations of the game. As the model avoids the reformulation in terms
of a constrained minimization problem it can be used for arbitrary payoff
functions with little calculational effort and provides a transparent and
simple formulation of the dynamics of the basic Minority Game in the asymmetric
phase
Nodal-antinodal dichotomy and magic doping fractions in a stripe ordered antiferromagnet
We study a model of a stripe ordered doped antiferromagnet consisting of
coupled Hubbard ladders which can be tuned from quasi-one-dimensional to
two-dimensional. We solve for the magnetization and charge density on the
ladders by Hartree-Fock theory and find a set of solutions with lightly doped
``spin-stripes'' which are antiferromagnetic and more heavily doped anti-phase
``charge-stripes''. Both the spin- and charge-stripes have electronic spectral
weight near the Fermi energy but in different regions of the Brillouin zone;
the spin-stripes in the ``nodal'' region, near (\pi/2,\pi/2), and the
charge-stripes in the ``antinodal'' region, near (\pi,0). We find a striking
dichotomy between nodal and antinodal states in which the nodal states are
essentially delocalized and two-dimensional whereas the antinodal states are
quasi-one-dimensional, localized on individual charge-stripes. For
bond-centered stripes we also find an even-odd effect of the charge periodicity
which could explain the non-monotonous variations with doping of the
low-temperature resistivity in LSCOComment: 6 pages, 6 figures, Expanded and improved, with additional reference
Suppression of superfluid stiffness near Lifshitz-point instability to finite momentum superconductivity
We derive the effective Ginzburg-Landau theory for finite momentum (FFLO/PDW)
superconductivity without spin population imbalance from a model with local
attraction and repulsive pair-hopping. We find that the GL free energy must
include up to sixth order derivatives of the order parameter, providing a
unified description of the interdependency of zero and finite momentum
superconductivity. For weak pair-hopping the phase diagram contains a line of
Lifshitz points where vanishing superfluid stiffness induces a continuous
change to a long wavelength Fulde-Ferrell (FF) state. For larger pair-hopping
there is a bicritical region where the pair-momentum changes discontinuously.
Here the FF type state is near degenerate with the Larkin-Ovchinnikov (LO) or
Pair-Density-wave (PDW) type state. At the intersection of these two regimes
there is a "Super-Lifshitz" point with extra soft fluctuations. The instability
to finite momentum superconductivity occurs for arbitrarily weak pair-hopping
for sufficiently large attraction suggesting that even a small repulsive
pair-hopping may be significant in a microscopic model of strongly correlated
superconductivity. Several generic features of the model may have bearing on
the cuprate superconductors, including the suppression of superfluid stiffness
in proximity to a Lifshitz point as well as the existence of subleading FFLO
order (or vice versa) in the bicritical regime
Band structure of Charge Ordered Doped Antiferromagnets
We study the distribution of electronic spectral weight in a doped
antiferromagnet with various types of charge order and compare to angle
resolved photoemission experiments on lightly doped LaSrCuO
(LSCO) and electron doped NdCeCuO. Calculations on
in-phase stripe and bubble phases for the electron doped system are both in
good agreement with experiment including in particular the existence of in-gap
spectral weight. In addition we find that for in-phase stripes, in contrast to
anti-phase stripes, the chemical potential is likely to move with doping. For
the hole doped system we find that ``staircase'' stripes which are globally
diagonal but locally vertical or horizontal can reproduce the photoemission
data whereas pure diagonal stripes cannot. We also calculate the magnetic
structure factors of such staircase stripes and find that as the stripe
separation is decreased with increased doping these evolve from diagonal to
vertical separated by a coexistence region. The results suggest that the
transition from horizontal to diagonal stripes seen in neutron scattering on
underdoped LSCO may be a crossover between a regime where the typical length of
straight stripe segments is longer than the inter-stripe spacing to one where
it is shorter and that locally the stripes are always aligned with the Cu-O
bonds.Comment: 13 pages, 16 figure
Lattice expansion from isotope substitution in the Iron based superconductors
We estimate the changes in lattice parameters due to iron isotope
substitution in the iron-based high temperature superconductors using a
variational calculation based on the anharmonicity of the Fe-As(Se) bond. For
BaFe2As2 and 57Fe to 54$Fe substitution we find a c-axis expansion of 1
10^{-3}{\AA} and in-plane a-axis contraction of 1 10^{-5}{\AA} at 250K in good
agreement with experimental values on (Ba,K)Fe2As2 for which a negative isotope
exponent \alpha=-\frac{d\ln T_c}{d\ln m}<0 was found [P.M. Shirage et al.,
Phys. Rev. Lett. 103, 257003 (2009)]. For FeSe in contrast we find an expansion
for both a and c lattice parameters. We discuss the relevance of these isotope
induced changes of lattice parameters to the isotope effect in light of the
well established sensitivity to the Fe-As(Se) coordination.Comment: 4 pages, 3 figure