Finite-Volume Spectra of the Lee-Yang Model

Abstract

We consider the non-unitary Lee-Yang minimal model $\mathcal{M}(2,5)$ in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels $(r,s)=(1,1),(1,2)$, (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply ${\phi }_{1,3}$ integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a ${\Phi }_{1,3}$ integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated $A_4$ RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of $(m,n)$ systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

LateX, 42 pages with 22 eps figures

References in corpus (3)

• Solving topological defects via fusion
• Finite volume form factors in the presence of integrable defects
• Approaching the RSOS critical points through entanglement: one model for many universalities

Cited by in corpus (10)

• Leading exponential finite size corrections for non-diagonal form factors
• Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations
• Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models
• Fused RSOS Lattice Models as Higher-Level Nonunitary Minimal Cosets
• OPE coefficients and the mass-gap from the integrable scattering description of 2D CFT's
• Yang-Baxter Integrable Dimers on a Strip
• Modular Properties of Generalised Gibbs Ensembles
• One-Dimensional Sums and Finitized Characters of $2\times 2$ Fused RSOS Models
• On the critical boundary RSOS \mathcal{M}(3,5) model
• Analytic structures of unitary RSOS models with integrable boundary conditions