量子Sine-Gordon模型平衡态和非平衡态的关联函数
Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium
摘要：
多点关联函数提供了关于量子场论（QFT）的平衡行为和动力学的完整信息。然而，它们的理论计算是一个具有挑战性的问题，即使是精确可解的模型。最近，由于模拟QFT模型和直接测量高阶关联的冷原子实验的进展，这已经成为一个实验相关的问题。在这里，我们计算关联函数的量子sine-Gordon模型，原型可积模型的中心利益，从理论和实验的角度来看。建立在所谓的截断共形空间方法，我们在数值上构建高阶相关性在有限大小的系统中的各种物理状态的实验相关性，无论是在平衡和不平衡。我们测量偏离高斯由于相互作用的存在，并分析其对温度的依赖性，解释实验观察到的高斯和非高斯制度之间的交叉。我们发现激发态的关联与热态的关联有很大的不同，这可以用系统的可积性来解释。我们还研究了动力学淬火后，观察的相互作用的关联函数，它们的空间依赖性的时间演化的影响，和它们的非高斯性测量的峰度。
英文摘要：
Complete information on the equilibrium behaviour and dynamics of a quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. This has recently become an experimentally relevant problem, due to progress in cold-atom experiments simulating QFT models and directly measuring higher order correlations. Here we compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental points of view. Building upon the so-called Truncated Conformal Space Approach, we numerically construct higher order correlations in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We measure deviations from Gaussianity due to the presence of interaction and analyse their dependence on temperature, explaining the experimentally observed crossover between Gaussian and non-Gaussian regimes. We find that correlations of excited states are markedly different from the thermal case, which can be explained by the integrability of the system. We also study dynamics after a quench, observing the effects of the interaction on the time evolution of correlation functions, their spatial dependence, and their non-Gaussianity as measured by the kurtosis.
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