430 research outputs found
Vacancy-induced low-energy states in undoped graphene
We demonstrate that a nonzero concentration nv of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ε=0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that wremains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on nv and correlations between vacancy positions. For low, but not-too-low, |ε|/t in this compensated case, we show that the density of states ρ(ε) exhibits a strong divergence of the form ρ_(Dyson)(ε)∼|ε|^(-1)/[log(t/|ε|)]^((y+1)), which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρ_(GW)(ε)∼|ε|^(-1)e^(-b[log(t/|ε|)]2/3) below a crossover scale ε_c≪t. ε_c is found to decrease rapidly with decreasing nv, while y decreases much more slowly
Vacancy-induced spin texture in a one dimensional Heisenberg antiferromagnet
We study the effect of a missing spin in a one dimensional
antiferromagnet with nearest neighbour Heisenberg exchange and six-spin
coupling using Quantum Monte-Carlo (QMC) and bosonization techniques.
For , the system is in a quasi-long range ordered
power-law antiferromagnetic phase, which gives way to a valence-bond solid
state that spontaneously breaks lattice translation symmetry for . We
study the ground state spin texture in the the ground state
of the system with a missing spin, focusing on the alternating
part . We find that our QMC results for at take on the
scaling form expected from bosonization considerations, but violate scaling for
. Within the bosonization approach, such violations of scaling arise
from the presence of a marginally irrelevant sine-Gordon interaction, whose
effects we calculate using renormalization group (RG) improved perturbation
theory. Our field-theoretical predictions are found to agree well with the QMC
data for .Comment: 9 pages, two-column PRB forma
Symmetry breaking perturbations and strange attractors
The asymmetrically forced, damped Duffing oscillator is introduced as a
prototype model for analyzing the homoclinic tangle of symmetric dissipative
systems with \textit{symmetry breaking} disturbances. Even a slight fixed
asymmetry in the perturbation may cause a substantial change in the asymptotic
behavior of the system, e.g. transitions from two sided to one sided strange
attractors as the other parameters are varied. Moreover, slight asymmetries may
cause substantial asymmetries in the relative size of the basins of attraction
of the unforced nearly symmetric attracting regions. These changes seems to be
associated with homoclinic bifurcations. Numerical evidence indicates that
\textit{strange attractors} appear near curves corresponding to specific
secondary homoclinic bifurcations. These curves are found using analytical
perturbational tools
Vacancy-induced low-energy states in undoped graphene
We demonstrate that a nonzero concentration nv of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ε=0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that wremains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on nv and correlations between vacancy positions. For low, but not-too-low, |ε|/t in this compensated case, we show that the density of states ρ(ε) exhibits a strong divergence of the form ρ_(Dyson)(ε)∼|ε|^(-1)/[log(t/|ε|)]^((y+1)), which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρ_(GW)(ε)∼|ε|^(-1)e^(-b[log(t/|ε|)]2/3) below a crossover scale ε_c≪t. ε_c is found to decrease rapidly with decreasing nv, while y decreases much more slowly
Global Superdiffusion of Weak Chaos
A class of kicked rotors is introduced, exhibiting accelerator-mode islands
(AIs) and {\em global} superdiffusion for {\em arbitrarily weak} chaos. The
corresponding standard maps are shown to be exactly related to generalized web
maps taken modulo an ``oblique cylinder''. Then, in a case that the web-map
orbit structure is periodic in the phase plane, the AIs are essentially {\em
normal} web islands folded back into the cylinder. As a consequence, chaotic
orbits sticking around the AI boundary are accelerated {\em only} when they
traverse tiny {\em ``acceleration spots''}. This leads to chaotic flights
having a quasiregular {\em steplike} structure. The global weak-chaos
superdiffusion is thus basically different in nature from the strong-chaos one
in the usual standard and web maps.Comment: REVTEX, 4 Figures: fig1.jpg, fig2.ps, fig3.ps, fig4.p
Griffiths Effects in Random Heisenberg Antiferromagnetic S=1 Chains
I consider the effects of enforced dimerization on random Heisenberg
antiferromagnetic S=1 chains. I argue for the existence of novel Griffiths
phases characterized by {\em two independent dynamical exponents} that vary
continuously in these phases; one of the exponents controls the density of
spin-1/2 degrees of freedom in the low-energy effective Hamiltonian, while the
other controls the corresponding density of spin-1 degrees of freedom.
Moreover, in one of these Griffiths phases, the system has very different low
temperature behavior in two different parts of the phase which are separated
from each other by a sharply defined crossover line; on one side of this
crossover line, the system `looks' like a S=1 chain at low energies, while on
the other side, it is best thought of as a chain. A strong-disorder RG
analysis makes it possible to analytically obtain detailed information about
the low temperature behavior of physical observables such as the susceptibility
and the specific heat, as well as identify an experimentally accessible
signature of this novel crossover.Comment: 16 pages, two-column PRB format; 5 figure
Multicritical crossovers near the dilute Bose gas quantum critical point
Many zero temperature transitions, involving the deviation in the value of a
conserved charge from a quantized value, are described by the dilute
Bose gas quantum critical point. On such transitions, we study the consequences
of perturbations which break the symmetry down to in spatial
dimensions. For the case , , we obtain exact, finite temperature,
multicritical crossover functions by a mapping to an integrable lattice model.Comment: 10 pages, REVTEX 3.0, 2 EPS figure
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