$$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$-invariant non-compact boundary conditions for the XXZ spin chain

@article{Chernyak2022,
  title={\$\$ \{U\}\_\{\mathfrak\{q\}\}\{\mathfrak\{sl\}\}\_2 \$\$-invariant non-compact boundary conditions for the XXZ spin chain},
  author={Dmitry Chernyak and Azat M. Gainutdinov and H. Saleur},
  journal={Journal of High Energy Physics},
  year={2022}
}
Abstract We introduce new $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$ U q sl 2 -invariant boundary conditions for the open XXZ spin chain. For generic values of $$ \mathfrak{q} $$ q we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for $$ \mathfrak{q}={e}^{\frac{i\pi}{p}} $$ q = e iπ p a 2p-th root of unity — to its p-dimensional analogue. Both cases are parametrised by a continuous “spin” α ∈ ℂ.To… 

References

SHOWING 1-10 OF 66 REFERENCES

Curiosities at c=-2

Conformal field theory at $c=-2$ provides the simplest example of a theory with ``logarithmic'' operators. We examine in detail the $(\xi,\eta)$ ghost system and Coulomb gas construction at $c=-2$

Conformal boundary loop models

Topological defects in lattice models and affine Temperley-Lieb algebra

This paper is the first in a series where we attempt to define defects in critical lattice models that give rise to conformal field theory topological defects in the continuum limit. We focus mostly

Lattice W-algebras and logarithmic CFTs

This paper is part of an effort to gain further understanding of 2D logarithmic conformal field theories (LCFTs) by exploring their lattice regularizations. While all work so far has dealt with the

The Temperley–Lieb algebra and its generalizations in the Potts and XXZ models

We discuss generalizations of the Temperley–Lieb algebra in the Potts and XXZ models. These can be used to describe the addition of integrable boundary terms of different types. We use the

Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem

  • H. TemperleyE. Lieb
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1971
A transfer-matrix approach is introduced to calculate the 'Whitney polynomial’ of a planar lattice, which is a generalization of the ‘percolation’ and ‘colouring’ problems. This new approach turns

Modified quantum dimensions and re-normalized link invariants

Abstract In this paper we give a re-normalization of the Reshetikhin–Turaev quantum invariants of links, using modified quantum dimensions. In the case of simple Lie algebras these modified quantum

Symplectic Fermions

...