Lattice Approach to Excited TBA Boundary Flows: Tricritical Ising Model

Abstract

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields $\xi$ and $\eta$ which play the role of the perturbing boundary fields ${\varphi }_{1,3}$ and ${\varphi }_{1,2}$ inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.

11 pages, 3 figures, LaTeX; v2: some useful notations and one reference added; to appear in PLB

References in corpus (2)

• Minimal model boundary flows and c=1 CFT
• Excited TBA Equations I: Massive Tricritical Ising Model

Cited by in corpus (11)

• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states
• The two-boundary sine-Gordon model
• Supersymmetry in the boundary tricritical Ising field theory
• Integrable and Conformal Twisted Boundary Conditions for sl(2) A-D-E Lattice Models
• Exact ${\varphi }_{1,3}$ boundary flows in the tricritical Ising model
• Excited TBA Equations II: Massless Flow from Tricritical to Critical Ising Model
• Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields
• Critical RSOS and Minimal Models I: Paths, Fermionic Algebras and Virasoro Modules
• TBA boundary flows in the tricritical Ising field theory
• DLCQ String Spectrum from $\mathcal{N}=2$ SYM Theory
• Excited Boundary TBA in the Tricritical Ising Model