We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical $Z_2$ gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling $2/3$.

中文翻译：

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结合Z2Gauge理论的一维无旋费米子的受限相

我们研究了一维无旋转费米子与动力学相互作用的量子多体晶格系统 ${ž}_2$规范领域。规范场介导了费米子之间的远距离吸引力，从而将它们限制在玻色子二聚体中。在强耦合下，我们开发了具有紧急约束的此类二聚体的完全可解决的有效理论。即使在通用耦合和费米子密度下，该模型也可以重写为局部自旋链。使用密度矩阵重归一化组，该系统显示为形成卢廷格液体，表明尽管晶格费米子受到限制，但仍存在分数激发。在有限链中，我们观察到Friedel振荡周期加倍，这为该系统中的局限性实验检测铺平了道路。我们讨论了在相应的填充量中出现Mott阶段的可能性$2/3$。