发表机构
The Institute of Mathematical Sciences; Homi Bhabha National Institute; Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino（马哈拉施特拉数学科学研究所; 霍米·巴巴国立研究所; 伦敦国王学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种系统方案构建广义吉布斯系综的ODE/IM对应物，将其应用于李-杨共形场论手征部分，推导自旋5系综，验证其满足李-杨Y系统，结果与共形场论计算匹配，方案可推广至其他可积模型。
AI 中文摘要
我们提出了一种系统方案，用于构建广义吉布斯系综的ODE/IM对应物，并将其应用于李-杨共形场论的手征部分。我们将化学势编码到三次振荡器的形变中，通过要求大能量WKB周期精确再现相应热力学Bethe ansatz方程的驱动项，逐阶确定该形变；随后，次阶WKB周期作为预测结果给出局域守恒荷的形变本征值。我们针对该模型的两个态详细推导了自旋5系综：基态，属于与形变三次振荡器对偶的初级场φ的模；以及恒等模的初级场，其对偶的振荡器带有一个表观奇点（双极点，位置由平凡单值性条件确定）。在两种情况下，斯托克斯乘数均满足李-杨Y系统，且经检验的阶数内，形变本征值与独立共形场论计算结果匹配。基态能量所得级数的Borel重求和，在化学势的多个数量级上再现了数值TBA解。该方案仅依赖ODE/IM对应关系的一般特征，适用于其他可积模型中的广义吉布斯系综。
英文摘要
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.
Comments53 pages, 3 figures
