Numerical study of the chiral Z3 quantum phase transition in one spatial dimension
Numerical study of the chiral Z3 quantum phase transition in one spatial dimension
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DOI：
10.1103/physreva.98.023614
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发表时间：
2018-06
影响因子：
2.9
通讯作者：
R. Samajdar;Soonwon Choi;H. Pichler;M. Lukin;S. Sachdev
中科院分区：
文献类型：
--
作者：
R. Samajdar;Soonwon Choi;H. Pichler;M. Lukin;S. Sachdev
最近对被捕获的碱金属原子的一维链的实验[Bernien等人，Nature（伦敦）551，579（2017）]已经观察到与泵浦里德堡态的周期3排序的开始相关联的量子跃迁。这种自发的${\mathbb{Z}}_{3}$对称性破缺由Fendley等人提出的硬核玻色子约束模型描述[Phys. Rev. B 69，075106（2004）]。通过对称性论证，该跃迁属于${\mathbb{Z}}_{3}$手征钟模型的普适类，其参数同时保持时间反演和空间反演对称性。我们研究了这些模型中有序-无序转变的性质，并用精确对角化和密度矩阵重整化群技术数值计算了其临界指数。我们使用有限尺寸标度来确定动力学临界指数$z$和相关长度指数$\ensuremath{\nu}$。我们的分析提出了一个强耦合的通用之间的带隙状态与$z\ensuremath{\ne}1$过渡的唯一已知的实例，这意味着一个潜在的非共形临界场理论。
Recent experiments on a one-dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.