Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions

Abstract

The finite size spectrum of the critical ${\mathbb{Z}}_2$-staggered spin-$1/2$ XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact $SU(2,\mathbb{R})/U(1)$ Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.

arXiv comment34 pages

References in corpus (22)

• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Branes in the 2D black hole
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• The Partition Function of the Two-Dimensional Black Hole Conformal Field Theory
• An Intersecting Loop Model as a Solvable Super Spin Chain
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling
• Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain
• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model
• Integrability of the $D_n^2$ vertex models with open boundary
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• Integrable boundary conditions in the antiferromagnetic Potts model
• Lattice regularisation of a non-compact boundary conformal field theory
• New D_{n+1}^(2) K-matrices with quantum group symmetry
• Finite-size effects in the spectrum of the $OSp(3|2)$ superspin chain
• Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
• Spectral flow for an integrable staggered superspin chain
• The fine structure of the finite-size effects for the spectrum of the $OSp(n|2m)$ spin chain
• On the critical behaviour of the integrable $q$-deformed $OSp(3|2)$ superspin chain

Cited by in corpus (5)

• The Floquet Baxterisation
• Integrable boundary conditions for staggered vertex models
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum