发表机构
Freie Universität Berlin; Massachusetts Institute of Technology; The Abdus Salam International Center for Theoretical Physics (ICTP); Leinweber Institute for Theoretical Physics, Stanford University（柏林自由大学; 麻省理工学院; 阿卜杜斯·萨拉姆国际理论物理中心（ICTP）; 斯坦福大学莱恩韦伯理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出解析理论，证明1+1维Lifshitz量子临界点可诱导$U(1)$对称性自发破缺，并通过DMRG验证了长程有序与拉伸指数衰减行为。
AI 中文摘要
我们提出了最近提出的在1+1维Lifshitz量子临界点处自发$U(1)$对称性破缺现象的解析理论。低能场论包含两个周期标量$\theta$和$\phi$，它们之间存在Berry相位耦合，使得$\theta$与$U(1)$电荷密度$\partial_x \phi$成为正则共轭。在可控的大$N$极限内，我们证明了$U(1)$带电的相位顶点$e^{i\beta\theta}$发展出长程有序，而共轭顶点$e^{i\beta\phi}$则以拉伸指数形式衰减，满足$\log\langle e^{i\beta\phi(x)} e^{-i\beta\phi(0)}\rangle\propto-|\beta|^{4/3}|x|^{2/3}$。超越大$N$极限，我们给出了解析论证：只要Lifshitz场论的动力学指数满足$z\neq1$，它就支持$U(1)$长程有序，这一条件得到了现有计算的有力支持。我们使用有限尺寸和无限系统DMRG在具有$U(1) \rtimes \mathbb{Z}_2$对称性的巡游费米子链中检验了这些预测。在$\mathbb{Z}_2$铁磁转变处，链的自旋部分映射到Lifshitz场论。与解析预测一致，$U(1)$带电的自旋向列键算符$S_i^+S_{i+1}^+$表现出长程有序，而电子格林函数则呈现拉伸指数衰减。这些结果共同阐明了1+1维中临界性诱导的$U(1)$对称性破缺的机制和后果。
英文摘要
We present an analytic theory of the recently proposed phenomenon of spontaneous $U(1)$ symmetry breaking at 1+1D Lifshitz quantum critical points. The low-energy field theory contains two periodic scalars $θ$ and $ϕ$, with a Berry phase coupling that makes $θ$ canonically conjugate to the $U(1)$ charge density $\partial_x ϕ$. Within a controlled large-$N$ limit, we demonstrate that the $U(1)$-charged phase vertex $e^{iβθ}$ develops long-range order, while the conjugate vertex $e^{iβϕ}$ decays as a stretched exponential, $\log\langle e^{iβϕ(x)} e^{-iβϕ(0)}\rangle\propto-|β|^{4/3}|x|^{2/3}$. Going beyond the large-$N$ limit, we give an analytic argument that the Lifshitz field theory supports $U(1)$ long-range order provided its dynamical exponent satisfies $z\neq1$, a condition strongly supported by existing calculations. We test these predictions using finite-size and infinite-system DMRG in an itinerant-fermion chain with $U(1) \rtimes \mathbb{Z}_2$ symmetry. At the $\mathbb{Z}_2$ ferromagnetic transition, the spin sector of the chain maps to the Lifshitz field theory. Consistent with analytic predictions, the $U(1)$-charged spin-nematic bond operator $S_i^+S_{i+1}^+$ exhibits long-range order, while the electron Green's function shows stretched-exponential decay. Together, these results elucidate the mechanism and consequences of criticality-enabled $U(1)$ symmetry breaking in 1+1D.
