Santos Lea F, Rigol Marcos
Department of Physics, Yeshiva University, New York, New York 10016, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 1):031130. doi: 10.1103/PhysRevE.82.031130. Epub 2010 Sep 23.
We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest-neighbor hopping and interaction, and next-nearest-neighbor interaction. The latter breaks integrability and induces a ground-state superfluid to insulator transition. By full exact diagonalization, we study chaos indicators and few-body observables. We show that when different symmetry sectors are mixed, chaos indicators associated with the eigenvectors, contrary to those related to the eigenvalues, capture the onset of chaos. The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization. We also study the properties of the off-diagonal matrix elements of few-body observables in relation to the transition from integrability to chaos and from chaos to localization.
我们研究了在有限一维系统中,当接近可积点或接近原子极限时的局域化情况,以及混沌区域中对称性的混合,如何影响热化的开始。我们考虑了在半填充情况下具有最近邻跳跃和相互作用以及次近邻相互作用的硬核玻色子系统。后者破坏了可积性,并诱导了基态超流体到绝缘体的转变。通过完全精确对角化,我们研究了混沌指标和少体可观测量。我们表明,当不同对称性扇区混合时,与本征向量相关的混沌指标,与那些与本征值相关的指标相反,能够捕捉到混沌的开始。本征向量的复杂性以及少体可观测量的期望值的结果证实了在混沌区域本征态热化假设的有效性,从而也证实了热化的发生。我们还研究了少体可观测量的非对角矩阵元与从可积性到混沌以及从混沌到局域化转变相关的性质。