Generalised Gibbs Ensembles from the ODE/IM Correspondence: the Lee--Yang Model
Abstract
We introduce a systematic scheme for constructing the ODE/IM counterpart of generalised Gibbs ensembles, and apply it to the chiral sector of the Lee--Yang conformal field theory. We encode the chemical potentials in a deformation of the cubic oscillator, fixed order by order by requiring that the large-energy WKB period reproduces exactly the driving term of the corresponding thermodynamic Bethe ansatz equation; the subleading WKB periods then yield, as predictions, the deformed eigenvalues of the local conserved charges. We work out the spin-5 ensemble in detail for two states of the model: the ground state, in the module of the primary ϕ, dual to the deformed cubic oscillator, and the primary of the identity module, dual to the same oscillator supplemented by an apparent singularity, a double pole whose position is fixed by a trivial-monodromy condition. In both cases, the Stokes multiplier obeys the Lee--Yang Y-system, and the deformed eigenvalues match, to the orders checked, an independent conformal-field-theory computation. The Borel resummation of the resulting series for the ground-state energy reproduces the numerical TBA solution over many orders of magnitude in the chemical potential. The scheme relies only on general features of the ODE/IM correspondence and applies to generalised Gibbs ensembles in other integrable models.
Related
BibTeX
@misc{ashok2026generalised,
title = {{Generalised Gibbs Ensembles from the ODE/IM Correspondence: the Lee--Yang Model}},
author = {Sujay K. Ashok and Max Downing and Faisal Karimi and Adarsh Sudhakar and Roberto Tateo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10716},
eprint = {2610.10716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10716},
}
RIS
TY - UNPB
TI - Generalised Gibbs Ensembles from the ODE/IM Correspondence: the Lee--Yang Model
AU - Sujay K. Ashok
AU - Max Downing
AU - Faisal Karimi
AU - Adarsh Sudhakar
AU - Roberto Tateo
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10716
UR - https://arxiv.org/abs/2610.10716
AB - We introduce a systematic scheme for constructing the ODE/IM counterpart of generalised Gibbs ensembles, and apply it to the chiral sector of the Lee--Yang conformal field theory. We encode the chemical potentials in a deformation of the cubic oscillator, fixed order by order by requiring that the large-energy WKB period reproduces exactly the driving term of the corresponding thermodynamic Bethe ansatz equation; the subleading WKB periods then yield, as predictions, the deformed eigenvalues of the local conserved charges. We work out the spin-5 ensemble in detail for two states of the model: the ground state, in the module of the primary ϕ, dual to the deformed cubic oscillator, and the primary of the identity module, dual to the same oscillator supplemented by an apparent singularity, a double pole whose position is fixed by a trivial-monodromy condition. In both cases, the Stokes multiplier obeys the Lee--Yang Y-system, and the deformed eigenvalues match, to the orders checked, an independent conformal-field-theory computation. The Borel resummation of the resulting series for the ground-state energy reproduces the numerical TBA solution over many orders of magnitude in the chemical potential. The scheme relies only on general features of the ODE/IM correspondence and applies to generalised Gibbs ensembles in other integrable models.
ER -