Abstract
We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound states. We reproduce the expression for the free energy density and the finite size corrections to the energy of an excited state as well as the LeClair-Mussardo series for the one-point function for local operators.
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Notes
- 1.
There however is a class of two-point functions for which a single insertion is sufficient [9].
- 2.
In the case of the non-local operators the situation is even worse: their diagonal limit diverges as \(L^M\) where M is the number of the particle pairs.
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Acknowledgements
We thank Benjamin Basso for enlightening discussions, to Zoltan Bajnok for bringing to our attention ref. Reference [8]. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.
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Kostov, I., Serban, D., Vu, DL. (2018). TBA and Tree Expansion. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2. LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 255. Springer, Singapore. https://doi.org/10.1007/978-981-13-2179-5_6
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DOI: https://doi.org/10.1007/978-981-13-2179-5_6
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