208 research outputs found
Boundary Entropy Can Increase Under Bulk RG Flow
The boundary entropy log(g) of a critical one-dimensional quantum system (or
two-dimensional conformal field theory) is known to decrease under
renormalization group (RG) flow of the boundary theory. We study instead the
behavior of the boundary entropy as the bulk theory flows between two nearby
critical points. We use conformal perturbation theory to calculate the change
in g due to a slightly relevant bulk perturbation and find that it has no
preferred sign. The boundary entropy log(g) can therefore increase during
appropriate bulk flows. This is demonstrated explicitly in flows between
minimal models. We discuss the applications of this result to D-branes in
string theory and to impurity problems in condensed matter.Comment: 20 page
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
The statistical mechanics of thermally excited vortex lines with columnar
defects can be mapped onto the physics of interacting quantum particles with
quenched random disorder in one less dimension. The destruction of the Bose
glass phase in Type II superconductors, when the external magnetic field is
tilted sufficiently far from the column direction, is described by a poorly
understood non-Hermitian quantum phase transition. We present here exact
results for this transition in (1+1)-dimensions, obtained by mapping the
problem in the hard core limit onto one-dimensional fermions described by a
non-Hermitian tight binding model. Both site randomness and the relatively
unexplored case of bond randomness are considered. Analysis near the mobility
edge and near the band center in the latter case is facilitated by a real space
renormalization group procedure used previously for Hermitian quantum problems
with quenched randomness in one dimension.Comment: 23 pages, 22 figure
Phase diagram of an impurity in the spin-1/2 chain: two channel Kondo effect versus Curie law
We consider a magnetic s=1/2 impurity in the antiferromagnetic spin chain as
a function of two coupling parameters: the symmetric coupling of the impurity
to two sites in the chain and the coupling between the two sites .
By using field theory arguments and numerical calculations we can identify all
possible fixed points and classify the renormalization flow between them, which
leads to a non-trivial phase diagram. Depending on the detailed choice of the
two (frustrating) coupling strengths, the stable phases correspond either to a
decoupled spin with Curie law behavior or to a non-Fermi liquid fixed point
with a logarithmically diverging impurity susceptibility as in the two channel
Kondo effect. Our results resolve a controversy about the renormalization flow.Comment: 5 pages in revtex format including 4 embedded figures (using epsf).
The latest version in PDF format is available from
http://fy.chalmers.se/~eggert/papers/phase-diagram.pd
Vortex pinning by meandering line defects in planar superconductors
To better understand vortex pinning in thin superconducting slabs, we study
the interaction of a single fluctuating vortex filament with a curved line
defect in (1+1) dimensions. This problem is also relevant to the interaction of
scratches with wandering step edges in vicinal surfaces. The equilibrium
probability density for a fluctuating line attracted to a particular fixed
defect trajectory is derived analytically by mapping the problem to a straight
line defect in the presence of a space and time-varying external tilt field.
The consequences of both rapid and slow changes in the frozen defect
trajectory, as well as finite size effects are discussed. A sudden change in
the defect direction leads to a delocalization transition, accompanied by a
divergence in the trapping length, near a critical angle.Comment: 9 pages, 9 figure
Magnetic susceptibility of a CuO2 plane in the La2CuO4 system: I. RPA treatment of the Dzyaloshinskii-Moriya Interactions
Motivated by recent experiments on undoped La2CuO4, which found pronounced
temperature-dependent anisotropies in the low-field magnetic susceptibility, we
have investigated a two-dimensional square lattice of S=1/2 spins that interact
via Heisenberg exchange plus the symmetric and anti-symmetric
Dzyaloshinskii-Moriya anisotropies. We describe the transition to a state with
long-ranged order, and find the spin-wave excitations, with a mean-field
theory, linear spin-wave analysis, and using Tyablikov's RPA decoupling scheme.
We find the different components of the susceptibility within all of these
approximations, both below and above the N'eel temperature, and obtain evidence
of strong quantum fluctuations and spin-wave interactions in a broad
temperature region near the transition.Comment: 20 pages, 2 column format, 22 figure
Assessing the Performance of Sampling Designs for Measuring the Abundance of Understory Plants
Accurate estimation of responses of understory plants to disturbance is essential for understanding the efficacy of management activities. However, the ability to assess changes in the abundance of plants may be hampered by inappropriate sampling methodologies. Conventional methods for sampling understory plants may be precise for common species but may fail to adequately characterize abundance of less common species. We tested conventional (modified Whittaker plots and Daubenmire and point–line intercept transects) and novel (strip adaptive cluster sampling [SACS]) approaches to sampling understory plants to determine their efficacy for quantifying abundance on control and thinned-and-burned treatment units in Pinus ponderosa forests in western Montana, USA. For species grouped by growth-form and for common species, all three conventional designs were capable of estimating cover with a 50% relative margin of error with reasonable sample sizes (3–36 replicates for growth-form groups; 8–14 replicates for common species); however, increasing precision to 25% relative margin of error required sample sizes that may be infeasible (11–143 replicates for growth-form groups; 28–54 replicates for common species). All three conventional designs required enormous sample sizes to estimate cover of nonnative species as a group (29–60 replicates) and of individual less common species (62–118 replicates), even with a 50% relative margin of error. SACS was the only design that efficiently sampled less common species, requiring only 6–11% as many replicates relative to conventional designs. Conventional designs may not be effective for estimating abundance of the majority of forest understory plants, which are typically patchily distributed with low abundance, or of newly establishing nonnative plants. Novel methods such as SACS should be considered in investigations when cover of these species is of concern
Vortex pinning by a columnar defect in planar superconductors with point disorder
We study the effect of a single columnar pin on a dimensional array
of vortex lines in planar type II superconductors in the presence of point
disorder. In large samples, the pinning is most effective right at the
temperature of the vortex glass transition. In particular, there is a
pronounced maximum in the number of vortices which are prevented from tilting
by the columnar defect in a weak transverse magnetic field. Using
renormalization group techniques we show that the columnar pin is irrelevant at
long length scales both above and below the transition, but due to very
different mechanisms. This behavior differs from the disorder-free case, where
the pin is relevant in the low temperature phase. Solutions of the
renormalization equations in the different regimes allow a discussion of the
crossover between the pure and disordered cases. We also compute density
oscillations around the columnar pin and the response of these oscillations to
a weak transverse magnetic field.Comment: 12 pages, 5 figures, minor typos corrected, a new reference adde
Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain
We study the spin-1/2 chain with nearest neighbor () and
next-nearest neighbor () interactions in the regime , which is equivalent to two chains with a `zig-zag' interaction. In
the continuum limit, this system is described in term of two coupled level-1
WZW field theories. We illustrate its equivalence with four off-critical Ising
models (Majorana fermions). This description is used to investigate the opening
of a gap as a function of and the associated spontaneous breakdown
of parity. We calculate the dynamic spin structure factor near the wavevectors
accessible to the continuum limit. We comment on the nonzero string order
parameter and show the presence of a hidden
symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a
ferromagnetic interchain coupling, the model is conjectured to be critical,
with different velocities for the spin singlet and spin triplet excitations.Comment: 20 pages, RevTeX, 1 postscript figure. Minor corrections added,
resulting in different velocity renormalizations; no qualitative change in
conclusion
Haldane gap in the quasi one-dimensional nonlinear -model
This work studies the appearance of a Haldane gap in quasi one-dimensional
antiferromagnets in the long wavelength limit, via the nonlinear
-model. The mapping from the three-dimensional, integer spin Heisenberg
model to the nonlinear -model is explained, taking into account two
antiferromagnetic couplings: one along the chain axis () and one along the
perpendicular planes () of a cubic lattice. An implicit equation for
the Haldane gap is derived, as a function of temperature and coupling ratio
. Solutions to these equations show the existence of a critical
coupling ratio beyond which a gap exists only above a transition temperature
. The cut-off dependence of these results is discussed.Comment: 14 pages (RevTeX 3.0), 3 PostScript figures appended (printing
instructions included
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