Quantum field theory for the chiral clock transition in one spatial dimension
Quantum field theory for the chiral clock transition in one spatial dimension
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DOI：
10.1103/physrevb.98.205118
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Seth Whitsitt;R. Samajdar;S. Sachdev
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文献类型：
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作者：
Seth Whitsitt;R. Samajdar;S. Sachdev
我们描述了空间维d = 1的N态手性时钟模型中的量子相变。由于选择了保持时间反转和空间反转对称性的耦合，这种模型在最近关于一维捕获超冷碱原子链中泵浦里德伯态排序的实验研究中属于普适类。对于这样的耦合和N = 3，时钟模型被期望有一个直接的相位转变，从一个破缺的缺口相位到一个恢复了的缺口相位。跃迁的动力学临界指数z≠1，因此不能用相对论量子场论来描述。我们使用晶格对偶变换将跃迁映射到d = 1时玻色气体的跃迁，涉及在高维N -玻色子凝聚背景下单个玻色子凝聚的开始。我们提出了二维展开中玻色气体跃迁的强耦合场论的重整化群分析，其中4 - N为二维阶。在双环阶，我们找到了一个具有重整化群不动点的参数域，它可以描述直接相变。我们还对N = 3的晶格手性时钟和玻色气体模型进行了数值密度矩阵重整化群研究，发现了直接相变的良好证据，并获得了z和相关长度指数ν的估计。
We describe the quantum phase transition in the N -state chiral clock model in spatial dimension d = 1 . With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and N = 3 , the clock model is expected to have a direct phase transition from a gapped phase with a broken global ℤ N symmetry, to a gapped phase with the ℤ N symmetry restored. The transition has dynamical critical exponent z ≠ 1 , and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in d = 1 , involving the onset of a single boson condensate in the background of a higher-dimensional N -boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2 - d , with 4 - N chosen to be of order 2 - d . At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for N = 3 , finding good evidence for a direct phase transition, and obtain estimates for z and the correlation length exponent ν .