费米点拓扑决定扩展量子自旋链中的涌现共形临界性

中文摘要 AI 辅助

一维量子系统中的量子临界性以涌现共形场论（CFT）为特征，其中心荷计数独立的无能隙自由度。在该研究中，研究人员在具有竞争团簇相互作用、交换各向异性和横向磁场的扩展量子自旋链中，揭示了费米点拓扑、共形临界性与量子纠缠之间的直接对应关系。研究表明，由相互作用和磁场驱动的 Lifshitz 转变会产生具有有效中心荷 $c_{\ m eff}=1/2$、$1$、$3/2$、$2$ 和 $3$ 的共形临界相，其中包括 Ising 和 Luttinger 液体区共存的多临界点。重要的是，中心荷并非仅由晶格能隙关闭点或费米点的数量决定，而是由考虑晶格对称性、倒格点识别和模式等价性后，独立低能连续区的数量及其共形内容决定。因此，Lifshitz 转变可能使共形反常保持不变，或根据谱重构是否产生新的独立连续区来改变中心荷。实空间和动量空间纠缠谱提供了互补的微观特征，揭示了临界模式的共形内容和动量空间组织。该研究结果建立了将费米点拓扑与涌现 CFT 关联的微观框架，并展示了相互作用驱动的谱重构如何产生更高中心荷的临界性和非常规多临界行为。

英文摘要

Quantum criticality in one-dimensional quantum systems is characterized by emergent conformal field theories (CFTs), whose central charge counts independent gapless degrees of freedom. Establishing a microscopic connection between this universal conformal structure and the momentum-space topology of the underlying quasiparticle spectrum remains challenging. Here, we uncover a direct correspondence between Fermi-point topology, conformal criticality, and quantum entanglement in an extended quantum spin chain with competing cluster interactions, exchange anisotropy, and a transverse magnetic field. We show that interaction- and field-driven Lifshitz transitions generate conformal critical phases with effective central charges $c_{\rm eff}=1/2$, $1$, $3/2$, $2$, and $3$, including a multicritical point where Ising and Luttinger-liquid sectors coexist. Importantly, the central charge is not determined simply by the number of lattice gap closings or Fermi points, but by the number and conformal content of independent low-energy continuum sectors after accounting for lattice symmetries, reciprocal-lattice identifications, and mode equivalences. Thus, Lifshitz transitions may leave the conformal anomaly unchanged or modify the central charge depending on whether spectral reconstruction generates new independent continuum sectors. Real- and momentum-space entanglement spectra provide complementary microscopic signatures, revealing both the conformal content and momentum-space organization of critical modes. Our results establish a microscopic framework linking Fermi-point topology to emergent CFTs and show how interaction-driven spectral reconstruction can generate higher-central-charge criticality and unconventional multicritical behavior.

发表机构

• Department of Physics, University of Guilan（吉兰大学物理系）

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