Zeng Meng, Zhu Zheng, Wang Juven, You Yi-Zhuang
Department of Physics, University of California San Diego, La Jolla, California 92093, USA.
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev Lett. 2022 May 6;128(18):185301. doi: 10.1103/PhysRevLett.128.185301.
Lattice regularization of chiral fermions has been a long-standing problem in physics. In this Letter, we present the density matrix renormalization group simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multilayer Chern insulator, whose finite width implies the quantum system is effectively (1+1)D. By introducing two sets of carefully designed six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions.
手征费米子的格点正则化一直是物理学中一个长期存在的问题。在本快报中，我们展示了具有无反常手征U(1)对称性的(1 + 1)维手征费米子的3 - 4 - 5 - 0模型的密度矩阵重整化群模拟，该模型包含两个分别携带U(1)电荷3、4和5、0的左行费米子和右行费米子。遵循王 - 文手征费米子模型，我们在多层陈绝缘体的(2 + 1)维格点模型的窄条带的相对边界上实现了手征费米子及其镜像伙伴，其有限宽度意味着量子系统实际上是(1 + 1)维的。通过仅在镜像部分引入两组精心设计的六费米子局部相互作用，我们证明了镜像费米子可以通过超过临界强度的相互作用而产生能隙，且不破坏手征U(1)对称性，这是通过对称质量生成机制实现的。我们表明，相互作用驱动的能隙转变属于贝雷津斯基 - 科斯特利茨 - Thouless普适类。我们确定了转变前卢廷格参数的演化，这证实了转变恰好发生在相互作用项变为边缘项的点上。由于转变后镜像部分有能隙，我们验证了轻手征费米子部分的费米子仍然无隙，这提供了所需的手征费米子的格点正则化。
