Abstract We explore a Z 2 Hamiltonian lattice gauge theory in one spatial dimension with a coupling h, without imposing any Gauss' law constraint. We show that in our model h = 0 is a free deconfined quantum critical point containing massless fermions where all Gauss' law sectors are equivalent. The coupling h is a relevant perturbation of this critical point and fermions become massive due to confinement and chiral symmetry breaking. To study the emergent Gauss' law sectors at low temperatures in this massive phase we use a quantum Monte Carlo method that samples configurations of the partition function written in a basis in which local conserved charges are diagonal. We find that two Gauss' law sectors, related by particle-hole symmetry, emerge naturally. When the system is doped with an extra particle, many more Gauss's law sectors related by translation invariance emerge. Using results in the range 0.01 h ≤ 0.15 we find that three different mass scales of the model behave like h p where p ≈ 0.579 .

中文翻译：

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高斯定律在 1 + 1 维 Z2 格子规范理论中的出现

摘要 我们在没有强加任何高斯定律约束的情况下，在具有耦合 h 的一个空间维度上探索了 Z 2 哈密顿格规范理论。我们表明，在我们的模型中，h = 0 是一个包含无质量费米子的自由去限制量子临界点，其中所有高斯定律扇区都是等效的。耦合 h 是该临界点的相关扰动，并且费米子由于限制和手性对称性破坏而变得巨大。为了研究这个大规模相中低温下出现的高斯定律扇区，我们使用量子蒙特卡罗方法对以局部守恒电荷为对角线的基编写的配分函数的配置进行采样。我们发现通过粒子-空穴对称性相关的两个高斯定律扇区自然出现。当系统掺杂一个额外的粒子时，更多的高斯' 出现了与平移不变性相关的法律部门。使用 0.01 h ≤ 0.15 范围内的结果，我们发现模型的三个不同质量尺度的行为类似于 hp，其中 p ≈ 0.579 。