Stability of the Spectral Gap for Lattice Fermions
arXiv:2005.04548
Abstract
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.
arXiv comment54 pages, no figure, v2: One reference added, and minor corrections
References in corpus (4)
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- A short proof of stability of topological order under local perturbations
- Ground states in relatively bounded quantum perturbations of classical lattice systems
- Persistence of exponential decay and spectral gaps for interacting fermions