Canella G A, França V V
Institute of Chemistry, São Paulo State University, 14800-090, Araraquara, São Paulo, Brazil.
Sci Rep. 2019 Oct 25;9(1):15313. doi: 10.1038/s41598-019-51986-0.
We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength V, ii) the concentration of impurities C and iii) the particle density n. Our results reveal the absence of a critical potential intensity on the SIT driven by V, i.e. any small V suffices to decrease considerably the degree of entanglement: it drops ∼50% for V = -0.25t. We also find that entanglement is non-monotonic with the concentration C, approaching to zero for a certain critical value C. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density n. Our results show that the SIT driven by n or C has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition only when leading to full localization. In contrast, the SIT driven by V is never a first-order quantum phase transition independently on the type of localization reached.
我们利用纠缠来追踪由一维哈伯德模型描述的无序费米子超流体中的超流-绝缘体转变（SIT）。发现纠缠具有由以下因素驱动的SIT的显著特征：i）无序强度V，ii）杂质浓度C和iii）粒子密度n。我们的结果表明，由V驱动的SIT不存在临界势强度，即任何小的V都足以显著降低纠缠程度：对于V = -0.25t，纠缠程度下降约50%。我们还发现纠缠随浓度C是非单调的，在某个临界值C时趋近于零。发现这个临界浓度与一种特殊类型的局域化有关，这里称为完全局域化状态，对于特定密度n也可以达到这种状态。我们的结果表明，由n或C驱动的SIT，无论导致完全局域化还是普通局域化，都具有不同的性质：只有当导致完全局域化时，它才是一阶量子相变。相比之下，由V驱动的SIT无论达到何种局域化类型，都绝不是一阶量子相变。
