The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling

Abstract

We study the emergence of non-compact degrees of freedom in the low energy effective theory for a class of ${\mathbb{Z}}_2$-staggered six-vertex models. In the finite size spectrum of the vertex model this shows up through the appearance of a continuum of critical exponents. To analyze this part of the spectrum we derive a set of coupled nonlinear integral equations from the Bethe ansatz solution of the vertex model which allow to compute the energies of the system for a range of anisotropies and of the staggering parameter. The critical theory is found to be independent of the staggering. Its spectrum and density of states coincide with the $SL(2,\mathbb{R})/U(1)$ Euclidean black hole conformal field theory which has been identified previously in the continuum limit of the vertex model for a particular 'self-dual' choice of the staggering. We also study the asymptotic behaviour of subleading corrections to the finite size scaling and discuss our findings in the context of the conformal field theory.

28 pages, 14 figures

References in corpus (8)

• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• The XXZ model with anti-periodic twisted boundary conditions
• Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain
• Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• Continuum Limit of gl(M/N) Spin Chains
• Finite-size corrections for logarithmic representations in critical dense polymers

Cited by in corpus (28)

• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Integrable boundary conditions in the antiferromagnetic Potts model
• On the scaling behaviour of the alternating spin chain
• Lattice regularisation of a non-compact boundary conformal field theory
• The Floquet Baxterisation
• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
• Integrable boundary conditions for staggered vertex models
• An Ising-type formulation of the six-vertex model
• Finite-size effects in the spectrum of the $OSp(3|2)$ superspin chain
• Spectral flow for an integrable staggered superspin chain
• Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
• The fine structure of the finite-size effects for the spectrum of the $OSp(n|2m)$ spin chain
• On the scaling behaviour of an integrable spin chain with ${\mathcal{Z}}_r$ symmetry
• On the critical behaviour of the integrable $q$-deformed $OSp(3|2)$ superspin chain
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• Exact solution of a anisotropic $J_1-J_2$ spin chain with antiperiodic boundary condition
• Spin chains with boundary inhomogeneities
• Exact solution of an integrable anisotropic $J_1-J_2$ spin chain model
• Stationary measure for six-vertex model on a strip
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-$\frac{1}{2}$ chain
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models