Automorphic equivalence within gapped phases of infinitely extended fermion systems
Mathematical Physics
2025-08-08 v2 math.MP
Quantum Physics
Abstract
We prove automorphic equivalence within gapped phases of infinitely extended lattice fermion systems (as well as spin systems) with super-polynomially decaying interactions. As a simple application, we prove a version of Goldstone's theorem for such systems: if an infinite volume interaction is invariant under a continuous symmetry, then any gapped ground state is also invariant under that symmetry.
Cite
@article{arxiv.2507.13321,
title = {Automorphic equivalence within gapped phases of infinitely extended fermion systems},
author = {Lennart Becker and Stefan Teufel and Marius Wesle},
journal= {arXiv preprint arXiv:2507.13321},
year = {2025}
}
Comments
23 pages; v2: differentiability assumptions for the Hamiltonian have been weakened