String order and symmetries in quantum spin lattices

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field -- defined on the space of closed loops -- that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in …

Symmetries and Strings of Adjoint QCD${}_2$

We revisit the symmetries of massless two-dimensional adjoint QCD with gauge group $SU(N)$. The dynamics is not sufficiently constrained by the ordinary symmetries and anomalies. Here we show that the theory in fact admits $\sim 2^{2N}$ non-invertible symmetries which severely constrain the possible infrared phases and massive excitations. We prove that for all $N$ these new symmetries enforce deconfinement of the fundamental quark. When the adjoint quark has a small mass, $m\ll g_\mathrm{YM}$, the theory confines and the non-invertible symmetries are softly broken. We use them to compute anal…

涌现高阶对称性下拓扑相变中 Fredenhagen-Marcu 弦序参量的临界行为

Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries

本研究利用 iPEPS 计算磁场下 toric code 的 FM 弦序参量，发现其在电荷凝聚相变临界点附近展现普适标度行为，且仅在存在涌现 1-form 对称性时才能忠实探测拓扑相变。

(2+1)维拓扑有序中的非可逆规范对称性：弦网模型实现

Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization

本文提出了一种基于弦网模型的研究方法，揭示了(2+1)维拓扑有序中首个非可逆范畴规范对称性，即双Fibonacci拓扑有序的Fibonacci规范对称性。