量子非谐链在非零温度下的Rényi熵
Rényi entropy of quantum anharmonic chain at non-zero temperature
AI总结：
本文提出基于路径积分Langevin动力学的新算法高效计算Rényi熵，解析了$\phi^4$模型非谐链的完整相图，发现有限温度下三个区域及Rényi熵发散与交叉线合并，确认相变属于二维Ising普适类。
摘要：
在量子临界点（QCP）附近，量子涨落与经典涨落的相互作用产生了具有不同量子特性的各种区域或相。在这项工作中，我们表明Rényi熵是表征临界系统相图的宝贵工具，不仅适用于QCP附近，也适用于远离QCP的区域，这得益于其检测有限温度下局域序出现的能力。为了高效计算Rényi熵，我们引入了一种基于路径积分Langevin动力学的新算法，并结合了先前提出的基于正则化路径的热力学积分方法。我们将此框架应用于研究非谐振荡器线性链的临界行为，这是$\phi^4$模型的一个特定实现。我们完全解析了其作为温度和相互作用强度函数的相图。在有限温度下，随着相互作用增强，我们发现了三个区域的序列——顺电相、无序相和准长程有序相。Rényi熵的发散与顺电相和无序相之间的交叉重合，该交叉不依赖于温度。另一方面，准长程有序的出现依赖于温度。两条交叉线在零温度下的QCP附近合并，此时Rényi熵出现尖锐峰值。通过其子系统尺寸标度，我们确认该相变属于二维Ising普适类。这一现象预计会出现在所有$\phi^4$类系统中，以及难以捉摸的水冰在VII、VIII和X相之间的转变中。
英文摘要：
The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the Rényi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the Rényi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the $ϕ^4$ model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes - para, disordered and quasi long-range ordered -, met as the interaction is increased. The Rényi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the Rényi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all $ϕ^4$-like systems, as well as in the elusive water ice transition across phases VII, VIII and X.
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