一维格点规范理论中动力学荷的禁闭和Mott跃迁
Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
摘要：
当物质与规范场耦合时，禁闭是一种普遍存在的现象，它表现为两个静电荷之间的线性弦势。虽然规范场可以在一维中积分，但它们可以介导非局域相互作用，从而影响典型的Luttinger液体性质。然而，当电荷变成动态的并且它们的密度有限时，理解限制变得具有挑战性。在这里，我们表明，禁闭在一维$\mathbb{Z}_2$格点规范理论，与动态物质场和任意密度，是有关的平移对称性破缺的非局部基础。这个字符串长度的基础上的精确变换，使我们想起路德-埃默里重新缩放的Luttinger参数的精确映射。我们包括当地的影响，但超越接触，物质粒子之间的相互作用，并表明，禁闭介子可以形成一个莫特绝缘状态时，解除限制的费用不能。虽然过渡到莫特状态不能检测到的格林函数的费用，我们表明，金属状态的特点是隐藏的非对角准长程序。我们的预测提供了新的见解的物理约束的动态电荷，并可以在实验上解决在光晶格中的里德伯装扮的量子气体。
英文摘要：
Confinement is an ubiquitous phenomenon when matter couples to gauge fields, which manifests itself in a linear string potential between two static charges. Although gauge fields can be integrated out in one dimension, they can mediate non-local interactions which in turn influence the paradigmatic Luttinger liquid properties. However, when the charges become dynamical and their densities finite, understanding confinement becomes challenging. Here we show that confinement in 1D $\mathbb{Z}_2$ lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a non-local basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery re-scaling. We include the effects of local, but beyond contact, interactions between the matter particles, and show that confined mesons can form a Mott-insulating state when the deconfined charges cannot. While the transition to the Mott state cannot be detected in the Green's function of the charges, we show that the metallic state is characterized by hidden off-diagonal quasi-long range order. Our predictions provide new insights to the physics of confinement of dynamical charges, and can be experimentally addressed in Rydberg-dressed quantum gases in optical lattices.
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