We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete ${\mathbb{Z}}_N$ symmetry predict that these are critical points with a $U(1)$ current algebra at $c=1$ and radius $\sqrt{2N}$ whenever $N>4$. We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models.

中文翻译：

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一维交错玻色子、时钟模型及其不可逆对称性


我们研究一维晶格中的交错玻色子哈密顿量系统，特别是这些系统中一个单元的平移对称性实际上是一种与 T 对偶性密切相关的不可逆对称性。我们还研究了从这些交错玻色子哈密顿量导出的最简单的时钟模型系统。我们证明了这些晶格模型的不可逆对称性以及离散 ${\mathbb{Z}}_N$ 对称性预测这些是临界点 $U(1)$ 当前代数为 $c=1$ 和半径 $\sqrt{2N}$ 每当 $N>4$ 。我们还提出了该值的独立计算，该值直接由交错玻色子变量产生，并且不使用这些额外的对称性。我们还提出了这些时钟模型中远离自对偶对称点的临界耦合常数值的理论估计。