论文标题
1+1尺寸手性费米3-4-5-0模型中的对称质量产生
Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
论文作者
论文摘要
手性费米子的晶格正规化一直是物理学的长期问题。在这项工作中，我们介绍了（DMRG）的密度矩阵重构化组（DMRG）模拟（1+1）d手性效费的3-4-5-0模型，具有无异常的手性u（1）对称性，其中包含两个左移动和两个右移动效率的fermions u（1）携带u（1）携带u（1）。遵循王的手性费米子模型，我们在多层Chern绝缘子的（2+1）D晶格模型的相对边界上实现手性费米子及其镜面伙伴，其有限的宽度意味着量子系统有效地（1+1）d。通过仅向镜像引入仔细设计的两组六个ferimion的局部相互作用，我们证明了镜像可以通过超出临界强度的相互作用来掩盖镜像，而不会通过对称质量产生（SMG）机制破坏手性u（1）对称性。我们表明，相互作用驱动的差距过渡在Berezinskii-Kosterlitz- thouless（BKT）通用类中。我们在过渡之前确定了Luttinger参数的演变，这证实了过渡完全发生在相互作用项变为边缘的点。由于镜像在过渡后盖上了镜像，因此我们检查光手性费米式扇形中的费米子是否保持无间隙，这提供了手性费米子的所需晶格正则化。
Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) 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 multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of 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 (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) 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.
