26 research outputs found
Adsorption on carbon nanotubes: quantum spin tubes, magnetization plateaus, and conformal symmetry
We formulate the problem of adsorption onto the surface of a carbon nanotube
as a lattice gas on a triangular lattice wrapped around a cylinder. This model
is equivalent to an XXZ Heisenberg quantum spin tube. The geometric frustration
due to wrapping leads generically to four magnetization plateaus, in contrast
to the two on a flat graphite sheet. We obtain analytical and numerical results
for the magnetizations and transition fields for armchair, zig-zag and chiral
nanotubes. The zig-zags are exceptional in that one of the plateaus has
extensive zero temperature entropy in the classical limit. Quantum effects lift
up the degeneracy, leaving gapless excitations which are described by a
conformal field theory with compactification radius quantized by the tube
circumference.Comment: 5 pages, 6 figure
Anomalous Quantum Diffusion at the Superfluid-Insulator Transition
We consider the problem of the superconductor-insulator transition in the
presence of disorder, assuming that the fermionic degrees of freedom can be
ignored so that the problem reduces to one of Cooper pair localization. Weak
disorder drives the critical behavior away from the pure critical point,
initially towards a diffusive fixed point. We consider the effects of Coulomb
interactions and quantum interference at this diffusive fixed point. Coulomb
interactions enhance the conductivity, in contrast to the situation for
fermions, essentially because the exchange interaction is opposite in sign. The
interaction-driven enhancement of the conductivity is larger than the
weak-localization suppression, so the system scales to a perfect conductor.
Thus, it is a consistent possibility for the critical resistivity at the
superconductor-insulator transition to be zero, but this value is only
approached logarithmically. We determine the values of the critical exponents
and comment on possible implications for the interpretation of
experiments
Non-equilibrium tunneling into general quantum Hall edge states
In this paper we formulate the theory of tunneling into general Abelian
fractional quantum Hall edge states. In contrast to the simple Laughlin states,
a number of charge transfer processes must be accounted for. Nonetheless, it is
possible to identify a unique value corresponding to dissipationless transport
as the asymptotic large- conductance through a tunneling junction, and find
fixed points (CFT boundary conditions) corresponding to this value. The
symmetries of a given edge tunneling problem determine the appropriate boundary
condition, and the boundary condition determines the strong-coupling operator
content and current noise.Comment: 6 pages, 3 figures; published versio
Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses
This article is a contribution to the understanding of fluctuations in the
out of equilibrium dynamics of glassy systems. By extending theoretical ideas
based on the assumption that time-reparametrization invariance develops
asymptotically we deduce the scaling properties of diverse high-order
correlation functions. We examine these predictions with numerical tests in a
standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system
where time-reparametrization invariance is not expected to hold, the 2d
ferromagnetic Ising model, both at low temperatures. Our results enlighten a
qualitative difference between the fluctuation properties of the two models and
show that scaling properties conform to the time-reparametrization invariance
scenario in the former but not in the latter.Comment: 17 pages, 5 figure
Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
We study the coarsening dynamics of the three-dimensional random field Ising
model using Monte Carlo numerical simulations. We test the dynamic scaling and
super-scaling properties of global and local two-time observables. We treat in
parallel the three-dimensional Edward-Anderson spin-glass and we recall results
on Lennard-Jones mixtures and colloidal suspensions to highlight the common and
different out of equilibrium properties of these glassy systems.Comment: 18 pages, 21 figure
Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet
We introduce a lattice model for a classical doped two dimensional
antiferromagnet which has no quenched disorder, yet displays slow dynamics
similar to those observed in supercooled liquids. We calculate two-time spatial
and spin correlations via Monte Carlo simulations and find that for
sufficiently low temperatures, there is anomalous diffusion and
stretched-exponential relaxation of spin correlations. The relaxation times
associated with spin correlations and diffusion both diverge at low
temperatures in a sub-Arrhenius fashion if the fit is done over a large
temperature-window or an Arrhenius fashion if only low temperatures are
considered. We find evidence of spatially heterogeneous dynamics, in which
vacancies created by changes in occupation facilitate spin flips on
neighbouring sites. We find violations of the Stokes-Einstein relation and
Debye-Stokes-Einstein relation and show that the probability distributions of
local spatial correlations indicate fast and slow populations of sites, and
local spin correlations indicate a wide distribution of relaxation times,
similar to observ ations in other glassy systems with and without quenched
disorder.Comment: 12 pages, 17 figures, corrected erroneous figure, and improved
quality of manuscript, updated reference
Topological Quantum Glassiness
Quantum tunneling often allows pathways to relaxation past energy barriers
which are otherwise hard to overcome classically at low temperatures. However,
this is not always the case. In this paper we provide simple exactly solvable
examples where the barriers each system encounters on its approach to lower and
lower energy states become increasingly large and eventually scale with the
system size. If the environment couples locally to the physical degrees of
freedom in the system, tunnelling under large barriers requires processes whose
order in perturbation theory is proportional to the width of the barrier. This
results in quantum relaxation rates that are exponentially suppressed in system
size: For these quantum systems, no physical bath can provide a mechanism for
relaxation that is not dynamically arrested at low temperatures. The examples
discussed here are drawn from three dimensional generalizations of Kitaev's
toric code, originally devised in the context of topological quantum computing.
They are devoid of any local order parameters or symmetry breaking and are thus
examples of topological quantum glasses. We construct systems that have slow
dynamics similar to either strong or fragile glasses. The example with
fragile-like relaxation is interesting in that the topological defects are
neither open strings or regular open membranes, but fractal objects with
dimension .Comment: (18 pages, 4 figures, v2: typos and updated figure); Philosophical
Magazine (2011
Andreev reflection in the fractional quantum Hall effect
We study the reflection of electrons and quasiparticles on point-contact
interfaces between fractional quantum Hall (FQH) states and normal metals
(leads), as well as interfaces between two FQH states with mismatched filling
fractions. We classify the processes taking place at the interface in the
strong coupling limit. In this regime a set of quasiparticles can decay into
quasiholes on the FQH side and charge excitations on the other side of the
junction. This process is analogous to an Andreev reflection in
normal-metal/superconductor (N-S) interfaces.Comment: 10 pages, 5 embedded EPS figures. Final version as published in Phys.
Rev. B 56, 2012 (1997
Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes
We study XXZ Heisenberg models on frustrated triangular lattices wrapped
around a cylinder. In addition to having interesting magnetic phases, these
models are equivalent to Bose-Hubbard models that describe the physical problem
of adsorption of noble gases on the surface of carbon nanotubes. We find
analytical results for the possible magnetization plateau values as a function
of the wrapping vectors of the cylinder, which in general introduce extra
geometric frustration besides the one due to the underlying triangular lattice.
We show that for particular wrapping vectors , which correspond to the
zig-zag nanotubes, there is a macroscopically degenerate ground state in the
classical Ising limit. The Hilbert space for the degenerate states can be
enumerated by a mapping first into a path in a square lattice wrapped around a
cylinder (a Bratteli diagram), and then to free fermions interacting with a
single degree of freedom. From this model we obtain the spectrum in
the anisotropic Heisenberg limit, showing that it is gapless. The continuum
limit is a conformal field theory with compactification radius set
by the physical tube radius. We show that the compactification radius
quantization is exact in the projective limit, and that
higher order corrections reduce the value of . The particular case of a
tube, which corresponds to a 2-leg ladder with cross links, is
studied separately and shown to be gapped because the fermion mapped problem
contains superconducting pairing terms.Comment: 10 pages, 11 figure
Non-perturbative saddle point for the effective action of disordered and interacting electrons in 2D
We find a non-perturbative saddle-point solution for the non-linear sigma
model proposed by Finkelstein for interacting and disordered electronic
systems. Spin rotation symmetry, present in the original saddle point solution,
is spontaneously broken at one-loop, as in the Coleman-Weinberg mechanism. The
new solution is singular in both the disorder and triplet interaction
strengths, and it also explicitly demonstrates that a non-trivial ferromagnetic
state appears in a theory where the disorder average is carried out from the
outset.Comment: 4 pages, 1 figur