格点费米子谱隙的稳定性
Stability of the Spectral Gap for Lattice Fermions
摘要：
人们普遍认为，格点自由费米子的费米海基态以上的谱隙在一般的弱相互作用下是稳定的。最近，Hastings提出了一个新的有趣的想法来证明Majorana自由费米子的稳定性。他巧妙地使用马约拉纳费米子，使未受扰哈密顿的自由费米子部分被映射成一个挫折免费的形式。本文改进了Hastings的论证，给出了一般格点自由费米子在一般弱相互作用下费米海基态上的谱隙稳定性的完整证明.
英文摘要：
It is widely believed that the spectral gap above the Fermi sea ground state of lattice free fermions is stable against generic weak interactions. Quite recently, Hastings presented a new interesting idea to prove the stability for Majorana free fermions. He ingeniously used Majorana fermions so that the unperturbed Hamiltonian of the free fermion part is mapped into a frustration-free form. In this paper, we refine Hastings's argument, and give a complete proof of the stability of the spectral gap above the Fermi sea ground state against generic weak interactions for generic lattice free fermions.
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