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首页> 外文期刊>Physical Review, A. Atomic, molecular, and optical physics >Finite-size effects in global quantum quenches: Examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
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Finite-size effects in global quantum quenches: Examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model

机译：整体量子猝灭中的有限尺寸效应：谐波陷阱中的自由玻色子和一维Bose-Hubbard模型的示例

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We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the ti me-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the "thermalized" regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.
机译：我们基于简单的能量论证研究量子猝灭中的有限尺寸效应。在低于微观能级的激发光谱的低能部分和高能机制之间进行区分，可以使人们定义出一个在小淬灭极限内发散的颗粒交叉数。根据初始和最终基态之间的保真度，提出了另一个交叉数。可以使用适用于大于全光谱对角化的系统的基态技术来计算这两个标准。例如，研究了两种模型：一种模型具有在谐波陷阱中被淬灭的自由玻色子，其频率被猝灭;另一种是一维Bose-Hubbard模型，该模型是不可积分的，并且最近的研究已经发现了显着的非平衡行为。计算时间平均密度矩阵的对角线权重，并将从该对角线集合中获得的可观测值与统计集合中的可观测值进行比较。有人认为，以前在小猝灭状态中观察到的Bose-Hubbard模型的“热化”状态会遇到强大的有限尺寸效应，从而很难与统计集合进行全面比较。此外，我们表明，在有限尺寸系统上出现且对于大相互作用淬灭的非热态与平衡量子临界点的存在无关，而与原子极限内能谱的高能结构有关。其特征使人联想起从非相互作用极限到原子极限的淬灭。

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