77 research outputs found
Necessary and sufficient conditions for flat bands in -dimensional -band lattices with complex-valued nearest-neighbour hopping
We formulate the necessary and sufficient conditions for the existence of
dispersionless energy eigenvalues (so-called `flat bands') and their associated
compact localized eigenstates in -dimensional tight-binding lattices with
sites per unit cell and complex-amplitude nearest-neighbour tunneling
between the lattice sites. The degrees of freedom can be traded for
longer-range complex hopping in lattices with reduced dimensionality. We show
the conditions explicitly for , , and , and outline their systematic construction for arbitrary , .
If and only if the conditions are satisfied, then the system has one or more
flat bands. By way of an example, we obtain new classes of flat band lattice
geometries by solving the conditions for the lattice parameters in special
cases.Comment: 7 pages, 4 figure
Order Induced by Dilution in Pyrochlore XY Antiferromagnets
XY pyrochlore antiferromagnets are well-known to exhibit order-by-disorder
through both quantum and thermal selection. In this paper we consider the
effect of substituting non-magnetic ions onto the magnetic sites in a
pyrochlore XY model with generally anisotropic exchange tuned by a single
parameter . The physics is controlled by two points in this
space of parameters at which there are line modes in
the ground state and hence an ground state degeneracy intermediate
between that of a conventional magnet and a Coulomb phase. At each of these
points, single vacancies seed pairs of line defects. Two line defects carrying
incompatible spin configurations from different vacancies can cross leading to
an effective one-dimensional description of the resulting spin texture. In the
thermodynamic limit at finite density, we find that dilution selects a state
"opposite" to the state selected by thermal and quantum disorder which is
understood from the single vacancy limit. The latter finding hints at the
possibility that ErYTiO for small exhibits a second
phase transition within the thermally selected state into a
state selected by the quenched disorder.Comment: 14 pages, 12 figure
Competing Antiferromagnetic and Spin-Glass Phases in a Hollandite Structure
We introduce a simple lattice model with Ising spins to explain recent
experimental results on spin freezing in a hollandite-type structure. We argue
that geometrical frustration of the lattice in combination with
nearest-neighbour antiferromagnetic (AFM) interactions is responsible for the
appearance of a spin-glass phase in presence of disorder. We investigate this
system numerically using parallel tempering. The model reproduces the magnetic
behaviour of oxides with hollandite structure, such as
and presents a rich phenomenology: in absence of disorder three types of ground
states are possible, depending on the relative strength of the interactions,
namely AFM ordered and two different disordered, macroscopically degenerate
families of ground states. Remarkably, for sets of AFM couplings having an AFM
ground state in the clean system, there exists a critical value of the disorder
for which the ground state is replaced by a spin-glass phase while maintaining
all couplings AFM. To the best of our knowledge this is the only existing model
that presents this kind of transition with short-range AFM interactions. We
argue that this model could be useful to understand the relation between AFM
coupling, disorder and the appearance of a spin-glass phase.Comment: 8 pages, 7 figure
Localization of spin waves in disordered quantum rotors
We study the dynamics of excitations in a system of quantum rotors in
the presence of random fields and random anisotropies. Below the lower critical
dimension the system exhibits a quasi-long-range order with
a power-law decay of correlations. At zero temperature the spin waves are
localized at the length scale beyond which the quantum
tunneling is exponentially suppressed . At finite temperature the spin
waves propagate by thermal activation over energy barriers that scales as
. Above the system undergoes an order-disorder
phase transition with activated dynamics such that the relaxation time grows
with the correlation length as at finite
temperature and as in the vicinity
of the quantum critical point.Comment: 8 pages, 2 figures, revtex
Incommensurate, helical spin ground states on the Hollandite lattice
We present a model of classical Heisenberg spins on a Hollandite lattice,
which has been developed to describe the magnetic properties of
-MnO and similar compounds. The model has nearest neighbor
interacting spins, however the strength and the sign of spin-spin interactions
is anisotropic and depends on the nature of the bonds. Our analysis shows that
the Hollandite lattice supports four different incommensurate and helical
magnetic ground states depending on the relative strengths and signs of
spin-spin interactions. We show that the incommensurate helical ground states
appear due to the geometrical frustration present in the model. We demonstrate
that each of the four helical incommensurate magnetic phases are continuously
connected to four different collinear antiferromagnetic ground states as the
strength of spin-spin interaction along some bonds is increased. The present
results give support to the presence of helical states that have been
previously suggested experimentally for Hollandite compounds. We provide an
in-depth analysis of the magnetic form factors for each helical phase and
describe how it could be used to identify each of these phases in neutron
diffraction experiments.Comment: 11 pages, 8 figure
Revisiting the slow dynamics of a silica melt using Monte Carlo simulations
We implement a standard Monte Carlo algorithm to study the slow, equilibrium
dynamics of a silica melt in a wide temperature regime, from 6100 K down to
2750 K. We find that the average dynamical behaviour of the system is in
quantitative agreement with results obtained from molecular dynamics
simulations, at least in the long-time regime corresponding to the
alpha-relaxation. By contrast, the strong thermal vibrations related to the
Boson peak present at short times in molecular dynamics are efficiently
suppressed by the Monte Carlo algorithm. This allows us to reconsider silica
dynamics in the context of mode-coupling theory, because several shortcomings
of the theory were previously attributed to thermal vibrations. A mode-coupling
theory analysis of our data is qualitatively correct, but quantitative tests of
the theory fail, raising doubts about the very existence of an avoided
singularity in this system. We discuss the emergence of dynamic heterogeneity
and report detailed measurements of a decoupling between translational
diffusion and structural relaxation, and of a growing four-point dynamic
susceptibility. Dynamic heterogeneity appears to be less pronounced than in
more fragile glass-forming models, but not of a qualitatively different nature.Comment: 13 pages, 10 figures; to be published in Phys. Rev.
Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices
We study a disordered classical Heisenberg magnet with uniformly
antiferromagnetic interactions which are frustrated on account of their
long-range Coulomb form, {\em i.e.} in and in . This arises naturally as the limit of the
emergent interactions between vacancy-induced degrees of freedom in a class of
diluted Coulomb spin liquids (including the classical Heisenberg
antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a
novel variant of a disordered long-range spin Hamiltonian. Using detailed
analytical and numerical studies we establish that this model exhibits a very
broad paramagnetic regime that extends to very large values of in both
and . In , using the lattice-Green function based finite-size
regularization of the Coulomb potential (which corresponds naturally to the
underlying low-temperature limit of the emergent interactions between
orphan-spins), we only find evidence that freezing into a glassy state occurs
in the limit of strong coupling, , while no such transition seems to
exist at all in . We also demonstrate the presence and importance of
screening for such a magnet. We analyse the spectrum of the Euclidean random
matrices describing a Gaussian version of this problem, and identify a
corresponding quantum mechanical scattering problem.Comment: two-column PRB format; 17 pages; 24 .eps figure
Kraichnan model of passive scalar advection
A simple model of a passive scalar quantity advected by a Gaussian
non-solenoidal ("compressible") velocity field is considered. Large order
asymptotes of quantum-field expansions are investigated by instanton approach.
The existence of finite convergence radius of the series is proved, a position
and a type of the corresponding singularity of the series in the regularization
parameter are determined. Anomalous exponents of the main contributions to the
structural functions are resummed using new information about the series
convergence and two known orders of the expansion.Comment: 21 page
Crossover from stationary to aging regime in glassy dynamics
We study the non-equilibrium dynamics of the spherical p-spin models in the
scaling regime near the plateau and derive the corresponding scaling functions
for the correlators. Our main result is that the matching between different
time regimes fixes the aging function in the aging regime to
. The exponent is related to the one giving the
length of the plateau. Interestingly is quickly very small when one
goes away from the dynamic transition temperature in the glassy phase. This
gives new light on the interpretation of experiments and simulations where
simple aging was found to be a reasonable but not perfect approximation, which
could be attributed to the existence of a small but non-zero stretching
exponent.Comment: 7 pages+2 figure
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