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.

arXiv comment39 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

References in corpus (13)

• Review of AdS/CFT Integrability: An Overview
• Constructing the generalized Gibbs ensemble after a quantum quench
• Excited states by analytic continuation of TBA equations
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Excited states in some simple perturbed conformal field theories
• A Numerical Renormalization Group for Continuum One-Dimensional Systems
• Excited-state thermodynamics
• Structure constants for the D-series Virasoro minimal models
• On Structure Constants of $sl(2)$ Theories
• Truncated Conformal Space Approach for Perturbed Wess-Zumino-Witten $SU(2{)}_k$ Models
• On the renormalisation group for the boundary Truncated Conformal Space Approach
• Dynamical correlations and quantum phase transition in the quantum Potts model
• Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

Cited by in corpus (30)

• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• A Cheap Alternative to the Lattice?
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• A Conformal Truncation Framework for Infinite-Volume Dynamics
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory
• Quantum quenches in two spatial dimensions using chain array matrix product states
• Exploring Hamiltonian Truncation in $\mathbf{d}=2+1$
• Confinement in the q-state Potts model: an RG-TCSA study
• Kibble-Zurek mechanism in the Ising Field Theory
• RG boundaries and interfaces in Ising field theory
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Confinement and bound states of bound states in a transverse-field two-leg Ising ladder
• Emergent conservation laws and nonthermal states in the mixed-field Ising model
• Chiral entanglement in massive quantum field theories in 1+1 dimensions
• Exact finite volume expectation values of local operators in excited states
• The renormalized Hamiltonian truncation method in the large $E_T$ expansion
• Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field
• 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 and false vacuum decay on the Potts quantum spin chain
• Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field
• Inhomogeneous quantum quenches in the sine-Gordon theory