具有简单非厄米哈密顿量的一维晶格手征费米子的量子反常命运
Fate of Quantum Anomalies for 1d lattice chiral fermion with a simple non-Hermitian Hamiltonian
AI总结：
本文提出一个独立于二维体的一维晶格手征费米子模型，利用简单非厄米跃迁哈密顿量抑制相反手征的加倍模式，从而在低能下重现连续理论的手征反常和引力反常。
摘要：
人们普遍认为，1+1维的单一手征费米子模型无法单独在晶格上存在。这种晶格实现的障碍在于无法重现连续理论中手征费米子的量子反常。传统的规避方法是将这个反常的一维系统与一个处于拓扑非平凡态的二维体（bulk）相关联，作为后者的边界。在本文中，我们提出了一个位于一维空间晶格上的1+1维手征费米子模型，它“独立存在”——不与二维体相关联——并具有一个简单的非厄米跃迁哈密顿量。我们使用多种方法证明，该模型具有与连续理论中相同的手征反常和引力反常。此外，在适当的参数下，该模型的低能有效理论仍然是幺正手征费米子的场论。成功的关键原因在于，由于哈密顿量的非厄米性，通常具有相反手征的“加倍”费米子模式被迅速衰减掉。
英文摘要：
It is generally believed that the 1+1D model for a single chiral fermion does not exist by itself alone on lattice. The obstruction to such a lattice realization is the failure to reproduce the quantum anomalies of a chiral fermion in continuum. The conventional way to escape is to associate the anomalous 1d system with a 2d bulk, which is in a topologically non-trivial state, as the boundary of the latter. In this paper, we propose a 1+1D chiral fermion model on 1d spatial lattice, {standing alone} -- without being associated with a 2d bulk -- with a simple {non-Hermitian} hopping Hamiltonian. We demonstrate, using various methods, that the model possesses the same chiral anomaly and gravitational anomaly as in continuum theory. Furthermore, with appropriate parameters, the low energy effective theory of the model remains a field theory for unitary chiral fermions. The essential reason for the success is that the usual "doubled" fermion mode with opposite chirality is rapidly damped out because of non-Hermicity of the Hamiltonian.
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