隐秩序对保序性失序的复原力
Resilience of hidden order to symmetry-preserving disorder
摘要：
本文研究了两种典型无序自旋链模型：自旋为1/2的Ising团簇模型和自旋为1的XXZ海森堡链模型中非定域弦序的鲁棒性。在干净的情况下，它们都显示出从反铁磁到弦序的转变。应用一种保持哈密顿对称性的无序，我们发现在这两种模型中的过渡都持续存在。在无序的集团-伊辛模型中，我们可以研究过渡解析-通过应用最强耦合重整化群-和数值-通过利用可积性研究反铁磁和弦序参量。我们将模型映射到一个二次费米子链，其中的过渡出现在零能量边缘模式的数量的变化。我们还探索了它的零温度奇异性行为，并发现了从非奇异到奇异区域的过渡，在一个不同于分离非局部和局部有序的点。无序的海森堡链只能用数值方法来处理：通过基于MPS的模拟，我们能够通过对序参量的研究来定位反铁磁相和弦序相之间的过渡。最后，我们讨论了我们的研究结果与多体局域化的可能联系。
英文摘要：
We study the robustness of non-local string order in two paradigmatic disordered spin-chain models, a spin-1/2 cluster-Ising and a spin-1 XXZ Heisenberg chain. In the clean case, they both display a transition from antiferromagnetic to string order. Applying a disorder which preserves the Hamiltonian symmetries, we find that the transition persists in both models. In the disordered cluster-Ising model we can study the transition analytically -- by applying the strongest coupling renormalization group -- and numerically -- by exploiting integrability to study the antiferromagnetic and string order parameters. We map the model into a quadratic fermion chain, where the transition appears as a change in the number of zero-energy edge modes. We also explore its zero-temperature-singularity behavior and find a transition from a non-singular to a singular region, at a point that is different from the one separating non-local and local ordering.} The disordered Heisenberg chain can be treated only numerically: by means of MPS-based simulations, we are able to locate the existence of a transition between antiferromagnetic and string-ordered phase, through the study of order parameters. Finally we discuss possible connections of our findings with many body localization.
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