Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we investigate Hamiltonian lattice gauge theories defined in two-leg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local ${\mathbb{Z}}_N$ gauge symmetries. We study its phase diagram based on both an effective low-energy field theory and density matrix renormalization group simulations. For $N\ge 5$, an extended gapless Coulomb phase emerges, which is separated by a Berezinskii-Kosterlitz-Thouless phase transition from the surrounding gapped phase. Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.

中文翻译：

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梯形几何中的ZNlattice规范理论

从实现晶格规理论的模拟量子模拟的角度来看，梯形几何提供了一个有趣的游乐场，与超冷原子实验有关。在这里，我们研究在两腿阶梯中定义的哈密顿量规理论。我们考虑一个同时包含规范玻色子和希格斯物质自由度的模型${\mathbb{ž}}_{ñ}$规范对称性。我们基于有效的低能量场理论和密度矩阵重归一化组模拟研究其相图。对于$ñ\ge 5$，出现了一个扩展的无间隙库仑相，该相被周围的空缺相通过Berezinskii-Kosterlitz-Thouless相变所分隔。除了传统的约束和希格斯状态外，我们还观察到了一个新的四极区域，该区域是由梯形几何图形产生的。