Topological holography: Towards a unification of Landau and beyond-Landau physics
Topological holography: Towards a unification of Landau and beyond-Landau physics
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DOI：
10.21468/scipostphyscore.6.4.066
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发表时间：
2022-07
影响因子：
3.6
通讯作者：
Heidar Moradi;Seyed Faroogh Moosavian;A. Tiwari
中科院分区：
文献类型：
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作者：
Heidar Moradi;Seyed Faroogh Moosavian;A. Tiwari
我们勾勒出一个全息框架，试图统一朗道和超越-朗道量子相和相变的范例。该框架利用现代对对称性作为拓扑缺陷/算子的理解，使用拓扑顺序来组织具有一维整体对称性的量子系统的空间。全局对称性自然作为拓扑顺序的输入。特别地，我们全息地构造了弦算符代数(SOA)，它是具有一维给定对称性G的对称量子系统的基石。这暴露了作用于G对称量子系统空间的一个巨大的对偶网络。SOA有助于对有间隙相的分类以及它们对应的序参数和基态激发，而对偶性有助于导航和预测相图的各个角落，并解析地计算相变的普适性类别。这种方法的一个新奇之处在于，它平等地对待传统的朗道和非传统的拓扑相变，从而提供了这些看似不同的理解领域的全息统一。我们揭示了有间隙的相及其多临界点的一个新特征，我们称之为融合结构，它编码了关于哪些相和相变可以彼此双重的信息。此外，我们发现自对偶系统通常具有涌现的不可逆性，即超越群类对称性。我们将这些思想应用于具有有限阿贝尔群对称性的1+1d1+1d量子自旋链，使用2+1d2+1d中的拓扑有序系统。我们预测了各种具体自旋模型的相图，并解析地计算了非平凡量子相变的全共形谱，然后进行了数值验证。
We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of G-symmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to 1+1d1+1d quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in 2+1d2+1d. We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically.