标题： 交错费米子的量子化轴向电荷和手征异常 显示英文标题

标题： Quantized axial charge of staggered fermions and the chiral anomaly

摘要： 在具有有限维希尔伯特空间的交错费米子的1+1维超局部晶格哈密顿量中，存在两个守恒的、整数值的荷，在连续极限下流向无质量狄拉克费米子的矢量和轴向荷，并带有微扰异常。 这两个晶格荷中的每一个都生成一个普通的U(1)整体对称性，该对称性在算符上局部作用并且可以单独规范。有趣的是，它们在一个有限晶格上不交换并对易关系生成Onsager代数，但在连续极限下它们的对易关系趋于零。 手征异常由这个非阿贝尔代数匹配，这与尼尔森-二宫定理一致。 我们进一步证明了这两个守恒晶格荷的存在迫使低能相成为无隙的，这类似于连续场论中连续整体对称性的微扰异常的结果。 在玻色化后，这两个荷导致XX模型中的两个精确的U(1)对称性，并在自由玻色子共形场论中流向动量和缠绕对称性。 显示英文摘要

摘要： In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac fermion with a perturbative anomaly. Each of the two lattice charges generates an ordinary U(1) global symmetry that acts locally on operators and can be gauged individually. Interestingly, they do not commute on a finite lattice and generate the Onsager algebra, but their commutator goes to zero in the continuum limit. The chiral anomaly is matched by this non-abelian algebra, which is consistent with the Nielsen-Ninomiya theorem. We further prove that the presence of these two conserved lattice charges forces the low-energy phase to be gapless, reminiscent of the consequence from perturbative anomalies of continuous global symmetries in continuum field theory. Upon bosonization, these two charges lead to two exact U(1) symmetries in the XX model that flow to the momentum and winding symmetries in the free boson conformal field theory.