用于开放边界的Razumov-Stroganov优化方法
Refined Razumov-Stroganov conjectures for open boundaries
摘要：
最近有人证明了作用在链模式空间中的具有一个边界算子的马尔可夫哈密顿量的基态与纵横对称的交替符号矩阵（等价于具有特殊边界的网格上的全填充回路组态）有关，我们通过引入一个任意的边界参数扩展了这一猜想.我们表明，依赖于参数的基态是与精制垂直对称交替符号矩阵，即与规定的配置（分别规定FPL配置）在下一个到中心行。我们还猜想的马尔可夫哈密顿量与两个边界算子和任意系数的基态和一些双细化（依赖于两个参数）FPL配置之间的关系。我们的结果对于O（1）和XXZ模型的基态以及Raise和Peel模型的定态的研究可能是有用的。
英文摘要：
Recently it has been conjectured that the ground-state of a Markovian Hamiltonian, with one boundary operator, acting in a link pattern space is related to vertically and horizontally symmetric alternating-sign matrices (equivalently fully-packed loop configurations (FPL) on a grid with special boundaries).We extend this conjecture by introducing an arbitrary boundary parameter. We show that the parameter dependent ground state is related to refined vertically symmetric alternating-sign matrices i.e. with prescribed configurations (respectively, prescribed FPL configurations) in the next to central row. We also conjecture a relation between the ground-state of a Markovian Hamiltonian with two boundary operators and arbitrary coefficients and some doubly refined (dependence on two parameters) FPL configurations. Our conjectures might be useful in the study of ground-states of the O(1) and XXZ models, as well as the stationary states of Raise and Peel models.
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