Excited state TBA and renormalized TCSA in the scaling Potts model

Abstract

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S-matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.

39 pages, 5 eps figures. v2: reference added. v3: several misprints corrected, and an important step in the derivation of counter terms (in section 3.4.1) is explained in more detail

Cited by in corpus (14)

• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• Confinement and bound states of bound states in a transverse-field two-leg Ising ladder
• Exact finite volume expectation values of local operators in excited states
• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Baryon masses in the three-state Potts field theory in a weak magnetic field
• Predicting Excitonic Gaps of Semiconducting Single Walled Carbon Nanotubes From a Field Theoretic Analysis
• Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain
• Soliton confinement in the double sine-Gordon model
• OPE coefficients and the mass-gap from the integrable scattering description of 2D CFT's
• Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field
• Confinement and false vacuum decay on the Potts quantum spin chain
• Inhomogeneous quantum quenches in the sine-Gordon theory