Massless fermions on a half-space: the curious case of 2+1-dimensions

Author:

Biswas ShovonORCID,Semenoff Gordon W.

Abstract

Abstract Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break C P and T symmetries as well as Lorentz and conformal symmetry. We show that there is essentially one special case where a single species of fermion has C PT and the full Poincare and conformal symmetry of the boundary. We show that, with doubled fermions, there is a second special case which respects C PT but still violates Lorentz and conformal symmetry. This second special case is essentially the unique boundary condition where the Dirac operator has fermion zero mode edge states. We discuss how the edge states lead to exotic representations of scale, phase and translation symmetries and how imposing a symmetry requirement leads to edge ferromagnetism of the system. We prove that the exotic ferromagnetic representations are indeed carried by the ground states of the system perturbed by a class of interaction Hamiltonians which includes the non-relativistic Coulomb interaction.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Massless fermions and superconductivity of string-wall composites;Journal of High Energy Physics;2024-02-05

2. Boundary ferromagnetism in zigzag edged graphene;Journal of Mathematical Physics;2023-07-01

3. Fermions in boundary conformal field theory: crossing symmetry and E-expansion;Journal of High Energy Physics;2023-02-13

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