论文标题
Wronskian Bethe方程的完整性理性GL（M | N）旋转链
Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
论文作者
论文摘要
我们考虑在定义表示中考虑合理的可超对称性GL（M | n）自旋链，并证明了保守指控的交换代数（贝尔氏代数）与多项式环（wronskian代数）之间的同构，我们呼吁wrwerskian skian betonskian bethe bethe bethe bethe betonskian bethe betonskian beceian bections quintiatiatiation。这些方程与标准嵌套的伯特方程相反，仅接受任何不均匀性值的物理解决方案，并且我们证明，这些方程的代数求解溶液数量等于旋转链hilbert Space的维度（Modulo相关的symmetries）。 考虑了扭曲和无扭曲的周期性边界条件，同构陈述用作充分条件，即自旋链不均匀性$θ_\ ell $，$ \ ell = 1，\ ldots，l $满足$θ_\ ell+ell+ell+el+hbar \ hbar \ hbar \ hbar \neqθ_{\ ell'} $ for $ for $ for $ for for $ for Ell'解决方案的计数以两种独立的方式进行：通过计算Wronskian代数的特征，并通过在某些缩放机制中明确求解Bethe方程，并补充了证明代数数量的解决方案对于任何值的$θ_\ ell $相同。特别是，我们考虑$θ_ {\ ell+1}/θ_ {\ ell} \ gg 1 $对于无扭曲链，我们成功地提供了具有标准的Young tableaux的明确解决方案及其系统标记。
We consider rational integrable supersymmetric gl(m|n) spin chains in the defining representation and prove the isomorphism between a commutative algebra of conserved charges (the Bethe algebra) and a polynomial ring (the Wronskian algebra) defined by functional relations between Baxter Q-functions that we call Wronskian Bethe equations. These equations, in contrast to standard nested Bethe equations, admit only physical solutions for any value of inhomogeneities and furthermore we prove that the algebraic number of solutions to these equations is equal to the dimension of the spin chain Hilbert space (modulo relevant symmetries). Both twisted and twist-less periodic boundary conditions are considered, the isomorphism statement uses, as a sufficient condition, that the spin chain inhomogeneities $θ_\ell$, $\ell=1,\ldots,L$ satisfy $θ_\ell+\hbar\neqθ_{\ell'}$ for $\ell<\ell'$. Counting of solutions is done in two independent ways: by computing a character of the Wronskian algebra and by explicitly solving the Bethe equations in certain scaling regimes supplemented with a proof that the algebraic number of solutions is the same for any value of $θ_\ell$. In particular, we consider the regime $θ_{\ell+1}/θ_{\ell}\gg 1$ for the twist-less chain where we succeed to provide explicit solutions and their systematic labelling with standard Young tableaux.
