Locality of KMS states for infinite fermionic lattice systems
Abstract
We study how thermal equilibrium states of infinite fermionic lattices respond to perturbations of the Hamiltonian. Our main result concerns extensive perturbations of a chosen KMS state. We show that exponential decay of correlations and exponential local indistinguishability under the extensive perturbation yield stretched-exponential decay of correlations for the perturbed state. Neither the initial nor the perturbed state is required to be unique, allowing stability to be studied in the presence of phase coexistence. Our approach uses Quantum Belief Propagation (QBP), which we establish directly on the underlying C*-algebra. Combining QBP with Lieb--Robinson bounds, we show implications between decay of correlations, the principle that local perturbations perturb locally, and local indistinguishability, closing the cycle for perturbations of the tracial state under the stated decay, support and uniformity assumptions. For extensive perturbations under uniform clustering conditions, we also obtain a differentiable path of local equilibrium expectations and bound their change linearly in the interaction norm of the perturbation.
Related
- Ground States of Nonlinear Fermionic Systems: From Power-Law Interactions to Logarithmic Sobolev Inequality
- Cubic Nonlinear Schrödinger Systems and Orthonormal Fermionic Ground States in ℝ
- Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison
- Convex-Gaussianity of fermionic Gibbs states in perturbation theory
- Entangled measurements are necessary for optimal tomography of mixed fermionic Gaussian states and of bosonic Gaussian states near the vacuum
BibTeX
@misc{becker2026locality,
title = {{Locality of KMS states for infinite fermionic lattice systems}},
author = {Lennart Becker},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31858},
eprint = {2609.31858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31858},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Locality of KMS states for infinite fermionic lattice systems
AU - Lennart Becker
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31858
UR - https://arxiv.org/abs/2609.31858
AB - We study how thermal equilibrium states of infinite fermionic lattices respond to perturbations of the Hamiltonian. Our main result concerns extensive perturbations of a chosen KMS state. We show that exponential decay of correlations and exponential local indistinguishability under the extensive perturbation yield stretched-exponential decay of correlations for the perturbed state. Neither the initial nor the perturbed state is required to be unique, allowing stability to be studied in the presence of phase coexistence. Our approach uses Quantum Belief Propagation (QBP), which we establish directly on the underlying C^*-algebra. Combining QBP with Lieb--Robinson bounds, we show implications between decay of correlations, the principle that local perturbations perturb locally, and local indistinguishability, closing the cycle for perturbations of the tracial state under the stated decay, support and uniformity assumptions. For extensive perturbations under uniform clustering conditions, we also obtain a differentiable path of local equilibrium expectations and bound their change linearly in the interaction norm of the perturbation.
ER -