临界稠密聚合物的Baxter Q算子
The Baxter Q Operator of Critical Dense Polymers
摘要：
我们考虑临界致密聚合物${\cal L}_{1,2}$，对应于中心荷的对数共形场论$c=-2$。Baxter $Q$算子的一个优雅的分解得到的有限数量的晶格运动积分。在格点上直接引入了所有局域、非局域和对偶非局域对合荷，它们的连续极限与共形场论预言的表达式一致.在Temperley-Lieb代数的取值格上引入了一个高度非平凡的算子$Ψ(ν)$.该$Ψ$函数提供了由Bazhanov、Lukyanov和Zamolodchikov引入的类似函数的晶格离散化。还观察到$Q$算子的本征值如何在连续标度极限下再现谐振子的谱行列式。
英文摘要：
We consider critical dense polymers ${\cal L}_{1,2}$, corresponding to a logarithmic conformal field theory with central charge $c=-2$. An elegant decomposition of the Baxter $Q$ operator is obtained in terms of a finite number of lattice integrals of motion. All local, non local and dual non local involutive charges are introduced directly on the lattice and their continuum limit is found to agree with the expressions predicted by conformal field theory. A highly non trivial operator $Ψ(ν)$ is introduced on the lattice taking values in the Temperley Lieb Algebra. This $Ψ$ function provides a lattice discretization of the analogous function introduced by Bazhanov, Lukyanov and Zamolodchikov. It is also observed how the eigenvalues of the $Q$ operator reproduce the well known spectral determinant for the harmonic oscillator in the continuum scaling limit.
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