标题： 3+1维单时间反演不变对称性保护的狄拉克费米子的无定理 显示英文标题

标题： No-go theorem for single time-reversal invariant symmetry-protected Dirac fermions in 3+1d

摘要： 我们采用一种称为异常匹配的通用方法，推导出费米子格点模型的新无结果定理。 对于我们的主要结果，我们证明时间反演不变的3+1维格点系统（如狄拉克和外尔半金属）永远无法容纳一个低能对称性保护的狄拉克费米子（或节点），即它必须始终以更高多重态的形式出现，或者需要微调。 该定理适用于非相互作用和相互作用系统，只要电磁$U(1)_{V,{\rm UV}}$对称性是微观对称群$G_{\mathrm{UV}}$的正规子群；这一条件在物理$U(1)_{V,{\rm UV}}$保持的格点模型中非常普遍。 为了表明我们的定理是紧致的，我们还探讨了已知和新的系统，这些系统是无结果定理的反面，通过放弃某些假设得到，例如破坏时间反演对称性（磁性外尔半金属）、非紧致非在位$U(1)$（几乎局部狄拉克节点模型）、无对称性保护（微调狄拉克半金属），或多个低能狄拉克节点（时间反演不变的外尔和狄拉克半金属）。 我们还将明确证明，虽然该定理严格禁止单一的时间反演不变对称性保护的狄拉克节点，但在某些情况下允许其他奇数个狄拉克节点，例如在Fu-Kane-Mele金刚石晶格模型中的三个狄拉克节点。 这类似于针对奇数个不同电荷的手征费米子的Nielsen-Ninomiya定理，如果满足某些异常抵消条件，它们的格点实现是允许的。 显示英文摘要

摘要： We employ a general method, known as anomaly-matching, to derive new no-go theorems of fermionic lattice models. For our main result, we show that time-reversal invariant 3+1d lattice systems (such as Dirac and Weyl semimetals) can never admit a lone low-energy symmetry-protected Dirac fermion (or node), i.e., it must always come in higher muliplets or be fine-tuned. This theorem holds for both non-interacting and interacting systems as long as the electromagnetic $U(1)_{V,{\rm UV}}$ symmetry is a normal subgroup of the microscopic symmetry group $G_{\mathrm{UV}}$; a condition that is ubiquitous in physical $U(1)_{V,{\rm UV}}$ preserving lattice models. To show that our theorems are tight, we also explore both well-known and new systems that are converses of the no-go theorem, obtained by forfeiting certain assumptions such as a broken time-reversal symmetry (magnetic Weyl semimetal), a non-compact non-on-site $U(1)$ (almost local Dirac node model), no-symmetry protection (fine-tuned Dirac semimetal), or multiple low-energy Dirac nodes (time-reversal invariant Weyl and Dirac semimetals). We will also explicitly demonstrate that, while this theorem strictly prohibits single time-reversal invariant symmetry-protected Dirac node, it does allow for other odd numbers of Dirac nodes under certain circumstances, such as three Dirac nodes in the Fu-Kane-Mele diamond lattice model. This is akin to the Nielsen-Ninomiya theorem for an odd number of differently-charged chiral fermions, whose lattice realizations are allowed if certain anomaly cancellation conditions are met.