论文标题
$ t-v-v'$晶格费米型模型的交互驱动的两极分化在半填充时：新兴haldane阶段
Interaction driven polarization shift in the $t-V-V'$ lattice fermion model at half filling: emergent Haldane phase
论文作者
论文摘要
我们在半填充时在一个维度上研究$ t-v-v'$型号。众所周知，对于足够大的$ v $固定，随着$ v'$的变化，系统从电荷密度波变成了Luttinger液体，然后是键订单，然后是第二个电荷密度波相。我们发现，Luttinger液态进一步分为两个，将多体极化浆液相的不同值分开。在此阶段，极化的方差在热力学极限中是无限的，这意味着即使极化有所不同，也无法测量。但是，在Luttinger液体每一侧的间隙相中，极化具有不同的可测量值，这意味着拓扑结构的区别。关键区别在于，较大的$ v'$阶段是对称的链接对称，而小$ v'$一个是站点倒入对称的。我们表明，大$ v'$相位可能与$ s = 1 $旋转链有关，并展示了Haldane阶段的许多功能。纠缠频谱的最低状态在两种情况下显示出不同的归化性，我们还发现了大型$ v'$相位的弦顺序。我们还研究了在开放边界条件下的系统，并建议缺陷的数量与拓扑有关。
We study the $t-V-V'$ model in one dimension at half-filling. It is known that for large enough $V$ fixed, as $V'$ is varied, the system goes from a charge-density wave into a Luttinger liquid, then a bond-order, and then a second charge density wave phase. We find that the Luttinger liquid state is further split into two, separating parts with distinct values of the many-body polarization Berry phase. Inside this phase, the variance of the polarization is infinite in the thermodynamic limit, meaning that even if the polarization differs, it would not be measurable. However, in the gapped phases on each side of the Luttinger liquid, the polarization takes a different measurable value, implying topologically distinction. The key difference is that the large-$V'$ phases are link-inversion symmetric, while the small-$V'$ one is site-inversion symmetric. We show that large-$V'$ phase can be related to an $S=1$ spin chain, and exhibits many features of the Haldane phase. The lowest lying states of the entanglement spectrum display different degeneracies in the two cases, and we also find string order in the large-$V'$ phase. We also study the system under open boundary conditions, and suggest that the number of defects is related to the topology.
