晶格带边界间的精确自旋量子霍尔电流
Exact spin quantum Hall current between boundaries of a lattice strip
摘要：
采用非均匀可解格点模型，推导了有限宽格点上边界到边界边缘电流的精确表达式。这个电流是最近引入的一类准费米观测量的一个例子，试图严格证明临界二维晶格模型的标度极限的共形不变性。它也对应于由Chalker和Coddington引入的模型中自旋-量子霍尔跃迁处的自旋电流，并由Gruzberg，Ludwig和Read推广。我们的结果是从$q$变形的Knizhnik-Zamolodchikov方程的解导出的，并且用辛Toda格点波函数表示。
英文摘要：
Employing an inhomogeneous solvable lattice model, we derive an exact expression for a boundary-to-boundary edge current on a lattice of finite width. This current is an example of a class of parafermionic observables recently introduced in an attempt to rigorously prove conformal invariance of the scaling limit of critical two-dimensional lattice models. It also corresponds to the spin current at the spin-Quantum Hall transition in a model introduced by Chalker and Coddington, and generalized by Gruzberg, Ludwig and Read. Our result is derived from a solution of the $q$-deformed Knizhnik-Zamolodchikov equation, and is expressed in terms of a symplectic Toda-lattice wave-function.
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