Spectrum statistics in the integrable Lieb-Liniger model,Physical Review E

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Spectrum statistics in the integrable Lieb-Liniger model
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-15 , DOI: 10.1103/physreve.104.034212
Samy Mailoud ₁ , Fausto Borgonovi _{2,

3} , Felix M Izrailev _{1,

4}

Affiliation

We address the old and widely debated question of the spectrum statistics of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of one-dimensional interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is to reveal the characteristic properties of energy levels in dependence of the model parameters. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. By studying long-range correlations between energy levels, we found strong deviations from the predictions based on the assumption of pseudorandom character of the distribution of energy levels.

中文翻译：

可积 Lieb-Liniger 模型中的频谱统计量

我们通过对范式 Lieb-Liniger 模型的分析，解决了可积量子系统的频谱统计这一古老且广受争议的问题。这种一维相互作用玻色子的量子多体模型允许通过 Bethe ansatz 方法严格确定能谱，我们的兴趣是根据模型参数揭示能级的特征属性。使用分析和数值研究，我们表明光谱的特性在很大程度上取决于分析是针对全能谱还是针对具有固定总动量的单个子集进行的。我们表明，最近邻能量之间间距的泊松分布只能发生在一组具有固定总动量的能级上，相互作用强度既不太大也不太弱，并获得足够高的能量。通过研究能级之间的长期相关性，我们发现与基于能级分布的伪随机特征假设的预测存在很大偏差。

更新日期：2021-09-15

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