发表机构
Department of Physics, The University of Hong Kong（香港大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一晶格视角，通过高能区对称性破缺与低能区对称性恢复的嵌套结构，解释手征与宇称反常，并阐明量子化响应的保护机制。
AI 中文摘要
量子反常通常在连续场论中表述，其中正则化可能破坏经典对称性。在晶体中，紧致的布里渊区和能带的高能部分使得这种紫外完备化具有物理意义。本展望通过实现单一无质量狄拉克费米子的问题，发展了手征反常和宇称反常的统一晶格视角。其核心结构是一个有限低能区域，在该区域内相关对称性得到恢复，并嵌入到破坏对称性并完成晶格理论的高能部分中。在$1+1$和$3+1$维中，量子化的手征响应受费米面附近的局域手征对称性保护。在$2+1$维中，半整数霍尔响应属于具有镜面对称性的单一无质量狄拉克能带，而非显式破坏该对称性的一般有质量狄拉克绝缘体。在这两种情形下，晶格视角揭示了低能对称性如何从高能部分涌现，并保护反常且量子化的响应。结合这一统一视角，讨论了量子材料中近期的实验进展。
英文摘要
Quantum anomalies are usually formulated in continuum field theory, where regularization may violate a classical symmetry. In a crystal, the compact Brillouin zone and the high-energy bands make that ultraviolet completion physical. This Perspective develops a unified lattice view of chiral and parity anomalies through the problem of realizing a single massless Dirac fermion. The central motif is a finite low-energy region in which the relevant symmetry is restored, embedded in a high-energy sector that breaks the symmetry and completes the lattice theory. In $1+1$ and $3+1$ dimensions, the quantized chiral response is protected by local chiral symmetry near the Fermi surface. In $2+1$ dimensions, the half-integer Hall response belongs to a single massless Dirac band with mirror symmetry, not to a generic massive Dirac insulator that breaks the symmetry explicitly. In both cases the lattice perspective reveals how the low-energy symmetry emerges from the high-energy sector and protects the anomalous and quantized response. Recent experimental progress in quantum materials is discussed in light of this unified view.
Comments18 pages, 6 figures
