论文标题
1D晶格性手性武器的量子异常的命运，并具有简单的非热汉密尔顿
Fate of Quantum Anomalies for 1d lattice chiral fermion with a simple non-Hermitian Hamiltonian
论文作者
论文摘要
人们普遍认为，单性手性费米昂的1+1D模型本身并不存在于晶格上。这种晶格实现的障碍物是未能再现连续性手性费物的量子异常。逃脱的常规方法是将异常的1D系统与2D散装相关联，该系统处于拓扑非平凡状态，作为后者的边界。在本文中，我们在1D空间晶格上提出了一个1+1D手性费米的模型，{独立} - 而没有与2D散装相关联 - 与简单的{non-hermitian}跳汉密尔顿。我们使用各种方法证明，该模型具有与连续理论相同的手性异常和引力异常。此外，有了适当的参数，模型的低能量有效理论仍然是单一手性费米子的现场理论。成功的基本原因是，与哈密顿官的非热性，通常的“加倍”费米子模式被相反的手性迅速减弱。
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.
