发表机构
PSI Center for Scientific Computing, Theory and Data; Center for Theoretical Physics — a Leinweber Institute, Massachusetts Institute of Technology; Department of Physics and Astronomy, Purdue University; Purdue Quantum Science and Engineering Institute, Purdue University; RIKEN Center for Emergent Matter Science; Institut de Physique, EPF Lausanne（瑞士保罗谢勒研究所科学计算、理论与数据中心; 麻省理工学院莱因韦伯理论物理中心; 普渡大学物理与天文系; 普渡大学普渡量子科学与工程研究所; 理化学研究所涌现物质科学研究中心; 洛桑联邦理工学院物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究一维自旋-1/2量子系统中对称性破缺与拓扑的竞争协作，引入两类特定对称性哈密顿量，发现奇异临界性质及非常规多临界机制。
AI 中文摘要
我们研究一维自旋-1/2量子系统中自发对称性破缺与对称性保护拓扑的竞争与协作机制。引入两类具有$\boldsymbol{\text{Z}_2\times\text{Z}_2\times\text{Z}^T_2}$对称性的局域哈密顿量，其包含丰富的对称性破缺相，含或无能隙边界自旋，具体为6个长程有序有隙相（按$\text{Z}_2$对称性破缺模式分为$\text{FM}_{x,y,z}$和Neel$_{x,y,z}$）、对应的对称性保护拓扑相（$\text{FM}^{\text{SPT}}_{x,y}$和Neel$^{\text{SPT}}_{x,y}$），以及2个无能隙相（$\text{gFM}_z$和$\text{gNeel}_z$），后者具有非公度$\text{Z}^T_2$破缺的磁性长程序和中心电荷$\boldsymbol{\text{c}=1}$。竞争有隙相之间的直接相变可为连续或弱一级相变，连续相变线具有奇异临界性质：例如，由Tomonaga-Luttinger液体理论描述的Neel$_x$与Neel$_y$相之间的退禁闭量子临界点线，在Lifshitz三临界点处被$\text{gFM}_z$相终止，该三临界点处哈密顿量虽具有局域性和一维性，却自发破缺连续$\text{U}(1)$对称性，与Hohenberg-Mermin-Wagner-Coleman定理的朴素预期相悖；此外，具有不同$\text{Z}_2$对称性破缺的对称性保护拓扑相（如Neel$^{\text{SPT}}_x$与Neel$^{\text{SPT}}_y$）之间的临界线还保留低能边界自由度，实现对称性富集临界性（或无能隙SPT相）。本研究揭示了对称性破缺与拓扑的竞争产生有序临界相和多临界性的非常规机制。
英文摘要
We investigate how spontaneous symmetry breaking and symmetry-protected topology compete and cooperate in one-dimensional quantum spin-1/2 systems. We introduce two families of local Hamiltonians with $\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{T}_{2}$ symmetry which host a zoo of broken-symmetry phases with and without gapless boundary spins, namely, six long-range-ordered gapped phases that differ by their $\mathbb{Z}^{\,}_{2}$-symmetry-breaking patterns (FM$^{\,}_{x,y,z}$ and Neel$^{\,}_{x,y,z}$), their partner symmetry-protected topological phases (FM$^{\mathrm{SPT}}_{x,y}$ and Neel$^{\mathrm{SPT}}_{x,y}$), and two gapless phases (gFM$^{\,}_{z}$ and gNeel$^{\,}_{z}$) with incommensurate $\mathbb{Z}^{T}_{2}$-breaking magnetic long-range order and central charge $\mathsf{c}=1$. Direct transitions between competing gapped phases can be continuous or weakly first order. We demonstrate that continuous phase transition lines have exotic critical properties. For example, a line of deconfined quantum critical points (between the Neel$^{\,}_{x}$ and Neel$^{\,}_{y}$ phases) described by Tomonaga-Luttinger liquid theory is terminated by the gFM$^{\,}_{z}$ phase at a Lifshitz tricritical point which exhibits spontaneous breaking of the continuous U(1) symmetry despite the locality and one-dimensionality of the Hamiltonian, contrary to a naive expectation from the Hohenberg-Mermin-Wagner-Coleman theorem. Furthermore, critical lines between symmetry-protected topological phases with different $\mathbb{Z}^{\,}_{2}$-symmetry breaking (e.g., Neel$^{\mathrm{SPT}}_{x}$ and Neel$^{\mathrm{SPT}}_{y}$) additionally retain low-energy boundary degrees of freedom, realizing symmetry-enriched criticality (or a gapless SPT phase). Our results reveal unconventional mechanisms by which competing symmetry breaking and topology generate ordered critical phases and multicriticality.
Comments97 pages, 37 figures
