Lieb-Robinson bounds, automorphic equivalence and LPPL for long-range interacting fermions

2025/07/04 by Stefan Teufel, Teufel, Stefan, Tom Wessel +1 · 5 citations
Chemistry · Mathematics · #FOS: Physical sciences #Graph theory and applications #History and advancements in chemistry #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2507.03319

openalex publication_date 2025/07/04 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28

Abstract

We prove a Lieb-Robinson bound for lattice fermion models with polynomially decaying interactions, which can be used to show the locality of the quasi-local inverse Liouvillian. This allows us to prove automorphic equivalence and the local perturbations perturb locally (LPPL) principle for these systems. The proof of the Lieb-Robinson bound is based on the work of Else et al. (2020), and our results also apply to spin systems. We explain why some newer Lieb-Robinson bounds for long-range spin systems cannot be used to prove the locality of the quasi-local inverse Liouvillian, and in some cases may not even hold for fermionic systems.

Citations

• The generalized adiabatic theorem for extended lattice systems
• Automorphic equivalence within gapped phases of infinitely extended fermion systems
• Non-equilibrium almost-stationary states and linear response for gapped\n quantum systems
• Lieb-Robinson Bounds and the Exponential Clustering Theorem

Cited by

• The Lieb-Robinson condition and the Fréchet topology
• Automorphisms with growing generators
• The generalized adiabatic theorem for extended lattice systems
• Automorphic equivalence within gapped phases of infinitely extended fermion systems
• The index of a pair of pure states and the interacting integer quantum Hall effect
• A note on Hall conductance and Hall conductivity in interacting Fermion systems

Related

• Enhanced Lieb-Robinson bounds for commuting long-range interactions
• Lieb-Robinson bounds in the continuum via localized frames
• Locality in Quantum Systems
• The Lieb-Robinson condition and the Fréchet topology
• Automorphic equivalence within gapped phases of infinitely extended fermion systems