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Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories

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arxiv hep-th/9407117 v2 pith:WLL36FBI submitted 1994-07-19 hep-th cond-matnlin.SIsolv-int

C. Destri , H.J. de Vega This is my paper · ORCID
classification hep-thcond-matnlin.SIsolv-int
keywords nlieapproachfieldmodelsizeansatzbethechain
verification ladder T0 review T1 audit T2 compute T3 formal
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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 {\bf single} non-linear 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 $h_z$ and c) the sine-Gordon-massive Thirring model (sG-mT) in a periodic box of size $\b \equiv 1/T $ 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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Cited by 2 Pith papers

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  1. Entanglement asymmetry in the gapped XYZ spin-$\frac12$ chain

    cond-mat.stat-mech 2026-07 conditional novelty 8.0 of 10

    In the gapped XYZ chain, the Rényi entanglement asymmetry of a large interval is ½ log(πℓχzz) + log n/(2(n−1)), with χzz/M computed from sine-Gordon form factors.

  2. Minimal Models RG flows: non-invertible symmetries & non-perturbative description

    hep-th 2025-01 conditional novelty 6.0 of 10

    A three-parameter NLIE family is conjectured to encode exact ground-state energies for anomaly-matched RG flows between Virasoro minimal models, generalizing known integrable cases.

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