Unified approach to Thermodynamic Bethe Ansatz and finite size corrections for lattice models and field theories |
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| Institution: | 1. Dipartimento di Fisica, University di Milano and INFN, sezione di Milano, Via Celoria 16, 20133 Milan, Italy;2. Laboratoire de Physique Théorique et Hautes Energies, Laboratoire Associi au CNRS UA 280, Tour 16 1er étage, Uniuersiti Paris VI, 4 Place Jussieu, 75252 Paris cedez 05, France;1. Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudny, Moscow region, 141700, Russian Federation;2. ITEP, B.Cheremushkinskaya 25, Moscow 117218, Russian Federation;3. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russian Federation;4. Skolkovo Institute of Science and Technology, 143026 Moscow, Russian Federation;5. National Research University Higher School of Economics, Russian Federation;6. Institute of Biochemical Physics of Russian Academy of Sciences, Kosygina str. 4, 119334, Moscow, Russian Federation;1. National Research University Higher School of Economics, Russian Federation;2. Skolkovo Institute of Science and Technology, 143026 Moscow, Russian Federation;3. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991 Moscow, Russian Federation;4. ITEP, B. Cheremushkinskaya 25, Moscow 117218, Russian Federation;5. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, Moscow Region 141700, Russian Federation;1. Institute of Physics, University of Tokyo, Komaba, Tokyo 153-8902, Japan;2. Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette, France |
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| Abstract: | We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for magnetic chains and field theories that includes the finite size (and zero-temperature) calculations for lattice BA models. In all cases, the free energy follows by quadratures from the solution of a single nonlinear integral equation (NLIE) (a system of NLIE appears for nested BA). We derive the NLIE for: (a) the six-vertex model with twisted boundary conditions, (b) the XXZ chain in an external magnetic field hz and (c) the massive Thirring sine-Gordon model (mT-sG) in a periodic box of size β ≡ T-1 using the light-cone approach. This NLIE is solved by iteration in one regime (high T in the XXZ chain and low T in the sG-mT model). In the opposite (conformal) regime, the leading behaviors are obtained in closed form. Higher corrections can be derived from the Riemann-Hilbert form of the NLIE that we present. |
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