标题： 横向场伊辛量子比特链中自发破缺的非可逆对称性 显示英文标题

标题： Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains

摘要： \usepackage{iopams}最近的发展表明，对称性不必形成一个群，而是可以是非可逆的。 在这里，我们使用分析论证和数值证据来阐明非可逆对称性的自发对称性破缺如何与普通的可逆对称性破缺相似但又有区别。 我们考虑由群值量子位组成的二维链，其局部希尔伯特空间由有限群$G$的元素张成（当$G=\mathbb{Z}_2$时退化为普通的量子位）。 我们构建了具有 Rep($G$) 对称性的伊辛型横场哈密顿量，其生成元按照群$G$的不可约表示（irreps）的张量积相乘。 对于非阿贝尔的$G$，对称性是非可逆的。 在对称性破缺相中，闭链上每个不可约表示有一个基态。 对称性破缺可以通过局部序参量检测，但与可逆情况不同，不同的基态具有不同的纠缠模式。 我们证明，对于维度大于一的不可约表示，相应的基态表现出字符串序、纠缠谱简并，并且在开链上有无能隙边缘模式——这些特征通常与对称性保护的拓扑序有关。 因此，域壁激发态表现为其一维非阿贝尔任意子，具有非平凡的内部希尔伯特空间和融合规则。 我们的工作确定了现有量子硬件可以探测的非可逆对称性破缺的特性。 显示英文摘要

摘要： \usepackage{iopams} Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group $G$ (reducing to ordinary qubits when $G=\mathbb{Z}_2$). We construct Ising-type transverse-field Hamiltonians with Rep($G$) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group $G$. For non-Abelian $G$, the symmetry is non-invertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain -- features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with non-trivial internal Hilbert spaces and fusion rules. Our work identifies properties of non-invertible symmetry breaking that existing quantum hardware can probe.