Stability of the Spectral Gap for Lattice Fermions
Author:
Preprint
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.Keywords
All Related Versions
This publication has 9 references indexed in Scilit:
- The stability of free fermi HamiltoniansJournal of Mathematical Physics, 2019
- Persistence of Exponential Decay and Spectral Gaps for Interacting FermionsCommunications in Mathematical Physics, 2018
- Universality of the Hall Conductivity in Interacting Electron SystemsCommunications in Mathematical Physics, 2016
- Automorphic Equivalence within Gapped Phases of Quantum Lattice SystemsCommunications in Mathematical Physics, 2011
- A Short Proof of Stability of Topological Order under Local PerturbationsCommunications in Mathematical Physics, 2011
- Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum OrderPhysical Review Letters, 2006
- Spectral Gap and Exponential Decay of CorrelationsCommunications in Mathematical Physics, 2006
- Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice SystemsCommunications in Mathematical Physics, 2005
- Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chainsCommunications in Mathematical Physics, 1992