发表机构
Tianjin University（天津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过Fock空间表述检验二维大c共形场论中的广义本征态热化假设，证明前两个qKdV荷唯一确定本征态，并在次领头阶证伪其强形式，表明高能级期望值需微观信息。
AI 中文摘要
我们发展了一种Fock空间表述，将真空族准初级算符在任意最高权共形族的qKdV本征态中的期望值约化为自由玻色子问题，并利用该表述在具有大中心荷$c$的二维共形场论中检验广义本征态热化假设（GETH）。我们证明了前两个量子Korteweg--de Vries（qKdV）荷$Q_1$和$Q_3$除在$(c,\Delta)$平面中至多可数条曲线外消除了所有简并，其中$\Delta$是共形族的最高权，因此全qKdV同时本征态由$Q_1$和$Q_3$唯一确定。基于此，本文通过qKdV荷的无限塔，提供了在真空共形族中检验或证伪GETH一般形式（即在局部可观测量期望值意义上将qKdV本征态与广义吉布斯系综的热态等同）的近乎完整的工具包。GETH的一种更强形式，即某一确定能级的局部可观测量所有期望值应可由qKdV荷表达但不包含微观本征态信息，在大$c$展开的次领头阶被直接证伪。在真空族的第6和第8能级，qKdV荷同时本征态中准初级算符的期望值不受前有限个qKdV荷固定，需要本征态的微观信息。
英文摘要
We develop a Fock-space formulation that reduces expectation values of vacuum-family quasi-primaries in qKdV eigenstates of arbitrary highest-weight conformal families to a free-bosonic problem, and employ it to test the generalized eigenstate thermalization hypothesis (GETH), in 2D conformal field theories with large central charge $c$. We demonstrate that the first two quantum Korteweg--de Vries (qKdV) charges $Q_1$ and $Q_3$ lift all degeneracies except along at most countably many curves in the $(c,Δ)$ plane, where $Δ$ is the highest weight of the conformal family, so that the full-qKdV simultaneous eigenstates are unambiguously determined by $Q_1$ and $Q_3$. Based on this, a near-complete toolkit for testing in the vacuum conformal family or falsifying the general form of GETH, i.e. equating qKdV eigenstates and thermal states of the generalized Gibbs ensemble in the sense of expectations of local observables, is provided in this paper, through the infinite tower of qKdV charges. A stronger form of the GETH, namely that all expectations of local observables of a definite level should be expressible of qKdV charges but not contain microscopic eigenstate information, is directly falsified at subleading order in the large-$c$ expansion. At levels 6 and 8 in the vacuum family, expectation values of quasi-primaries in simultaneous eigenstates of the qKdV charges are not fixed by first finitely many qKdV charges, and microscopic information of the eigenstate is required.
