Spectral and Entanglement Properties of the Random Exchange Heisenberg Chain

Yilun Gao, Rudolf A. Römer
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Abstract

We study the many-body localization problem in the non-abelian SU(2)-invariant random anti-ferromagnetic exchange model in 1D. Exact and sparse matrix diagonalization methods are used to calculate eigenvalues and eigenvectors of the Hamiltonian matrix. We investigate the behaviour of the energy level gap-ratio statistic, participation ratio, entanglement entropy and the entanglement spectral parameter as a function of disorder strengths. Different distributions of random couplings are considered. We find, up to L = 18, a clear distinction between our non-abelian model and the more often studied random field Heisenberg model: the regime of seemingly localized behaviour is much less pronounced in the random exchange model than in the field model case.
随机交换海森堡链的谱和纠缠特性
我们研究了一维非阿贝尔SU(2)不变随机反铁磁交换模型中的多体定位问题。我们使用精确和稀疏矩阵对角化方法来计算哈密顿矩阵的特征值和特征向量。我们研究了能级间隙比统计量、参与比、纠缠熵和纠缠谱参数作为无序强度函数的行为。我们发现,在 L =18 以下,我们的非阿贝尔模型与更常被研究的随机场海森堡模型之间存在明显区别:随机交换模型中的看似局部行为的机制远没有场模型中的明显。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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