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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.

Keywords

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