Asia Pacific Center for Theoretical Physics, Pohang, 37673, Korea.
Department of Physics, POSTECH, Pohang, 37673, Korea.
Sci Rep. 2017 Jun 5;7(1):2745. doi: 10.1038/s41598-017-02717-w.
We investigate the quantum phase transition of the Su-Schrieffer-Heeger (SSH) model by inspecting the two-site entanglements in the ground state. It is shown that the topological phase transition of the SSH model is signified by a nonanalyticity of local entanglement, which becomes discontinuous for finite even system sizes, and that this nonanalyticity has a topological origin. Such a peculiar singularity has a universal nature in one-dimensional topological phase transitions of noninteracting fermions. We make this clearer by pointing out that an analogous quantity in the Kitaev chain exhibiting the identical nonanalyticity is the local electron density. As a byproduct, we show that there exists a different type of phase transition, whereby the pattern of the two-site entanglements undergoes a sudden change. This transition is characterised solely by quantum information theory and does not accompany the closure of the spectral gap. We analyse the scaling behaviours of the entanglement in the vicinities of the transition points.
我们通过检查基态中的两站点纠缠来研究 Su-Schrieffer-Heeger (SSH) 模型的量子相变。结果表明，SSH 模型的拓扑相变由局域纠缠的非连续性标志，对于有限的偶数系统大小，这种非连续性是不连续的，并且这种非连续性具有拓扑起源。这种特殊的奇异现象在一维无相互作用费米子的拓扑相变中具有普遍性。我们通过指出在表现出相同非连续性的 Kitaev 链中的类似量是局域电子密度，使这一点更加清晰。作为副产品，我们表明存在另一种类型的相变，其中两站点纠缠的模式发生突然变化。这种转变仅由量子信息理论描述，并不伴随着谱隙的闭合。我们分析了相变点附近纠缠的标度行为。
