English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

For general Temperley-Lieb loop models, including the logarithmic minimalmodels ${\cal LM}(p,p')$ with $p,p'$ coprime integers, we construct an infinitefamily of Robin boundary conditions on the strip as linear combinations ofNeumann and Dirichlet boundary conditions. These boundary conditions areYang-Baxter integrable and allow loop segments to terminate on the boundary.Algebraically, the Robin boundary conditions are described by the one-boundaryTemperley-Lieb algebra. Solvable critical dense polymers is the first member${\cal LM}(1,2)$ of the family of logarithmic minimal models and has loopfugacity $\beta=0$ and central charge $c=-2$. Specializing to ${\cal LM}(1,2)$with our Robin boundary conditions, we solve the model exactly on strips ofarbitrary finite size $N$ and extract the finite-size conformal correctionsusing an Euler-Maclaurin formula. The key to the solution is an inversionidentity satisfied by the commuting double row transfer matrices. Thisinversion identity is established directly in the Temperley-Lieb algebra. Weclassify the eigenvalues of the double row transfer matrices using the physicalcombinatorics of the patterns of zeros in the complex spectral parameter planeand obtain finitized characters related to spaces of coinvariants of$\mathbb{Z}_4$ fermions. In the continuum scaling limit, the Robin boundaryconditions are associated with irreducible Virasoro Verma modules withconformal weights $\Delta_{r,s-\frac{1}{2}}=\frac{1}{32}(L^2-4)$ where$L=2s-1-4r$, $r\in\mathbb{Z}$, $s\in\mathbb{N}$. These conformal weightspopulate a Kac table with half-integer Kac labels. Fusion of the correspondingmodules with the generators of the Kac fusion algebra is examined and generalfusion rules are proposed.

Critical dense polymers with Robin boundary conditions, half-integer Kac labels and $\mathbb{Z}_4$ fermions