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 $J_1$ and the coupling between the two sites $J_2$. 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 $(1+1)$ 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 ($\kappa_1$) and next-nearest neighbor ($\kappa_2$) interactions in the regime $\kappa_2\gg \kappa_1$, 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 $\kappa_1$ 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 ${\Bbb Z}_2\times{\Bbb Z}_2$ 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 σ\sigma-model

This work studies the appearance of a Haldane gap in quasi one-dimensional antiferromagnets in the long wavelength limit, via the nonlinear $\sigma$-model. The mapping from the three-dimensional, integer spin Heisenberg model to the nonlinear $\sigma$-model is explained, taking into account two antiferromagnetic couplings: one along the chain axis ($J$) and one along the perpendicular planes ($J_\bot$) of a cubic lattice. An implicit equation for the Haldane gap is derived, as a function of temperature and coupling ratio $J_\bot/J$. Solutions to these equations show the existence of a critical coupling ratio beyond which a gap exists only above a transition temperature $T_N$. The cut-off dependence of these results is discussed.Comment: 14 pages (RevTeX 3.0), 3 PostScript figures appended (printing instructions included