论文标题
一维离子哈伯德模型的水平统计数据
Level statistics of the one-dimensional ionic Hubbard model
论文作者
论文摘要
在这项工作中，我们分析了一维离子哈伯德模型的光谱水平统计数据，该模型是具有交替现场电位的哈伯德模型。特别是，我们关注连续能级之间的间隙比的统计数据。该数量通常用于发出多体系统是可集成还是混乱的。混沌系统通常具有随机矩阵的高斯集合的统计数据，而可集成系统的光谱特性则遵循泊松统计。我们发现，尽管没有交流电势的Hubbard模型是可集成的，并且其光谱特性遵循泊松统计，但交流电势的存在会导致光谱特性的急剧变化，类似于随机矩阵的高斯集团之一。但是，要揭示这种行为，必须单独考虑离子哈伯德模型所有对称性的块。
In this work we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive energy levels. This quantity is often used in order to signal whether a many-body system is integrable or chaotic. A chaotic system has typically the statistics of a Gaussian ensemble of random matrices while the spectral properties of the integrable system follow a Poisson statistics. We find that whereas the Hubbard model without alternating potential is known to be integrable and its spectral properties follow a Poissonian statistics, the presence of an alternating potential causes a drastic change in the spectral properties which resemble the one of a Gaussian ensemble of random matrices. However, to uncover this behavior one has to separately consider the blocks of all symmetries of the ionic Hubbard model.
