Area laws for free fermions in ergodic field: spectral criteria and localisation-based methods
Abstract
We review rigorous results concerning the Area Law for the entanglement entropy of free fermions whose one-body Hamiltonian is an ergodic Schrödinger operator with a strongly localised pure point spectrum. Particular attention is paid to operators with deterministic potentials (quasi-periodic ones and those generated by subshifts of finite type). Our approach relies on reducing the problem to obtaining exponential estimates for the eigenfunction correlator. This provides an effective route from localisation to the Area Law and allows for the identification of additional spectral estimates that need to be proven for various classes of ergodic operators. We realise this approach by using various localisation techniques, including dynamical localisation and the uniformly localised eigenfunction property for bounded and unbounded ergodic operators (e.g. the Maryland model), as well as a new method for obtaining the corresponding exponential bounds for Schrödinger operators generated by subshifts of finite type.
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BibTeX
@misc{pastur2026area,
title = {{Area laws for free fermions in ergodic field: spectral criteria and localisation-based methods}},
author = {Leonid Pastur and Mira Shamis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41845},
eprint = {2610.41845},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41845},
}
RIS
TY - UNPB
TI - Area laws for free fermions in ergodic field: spectral criteria and localisation-based methods
AU - Leonid Pastur
AU - Mira Shamis
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41845
UR - https://arxiv.org/abs/2610.41845
AB - We review rigorous results concerning the Area Law for the entanglement entropy of free fermions whose one-body Hamiltonian is an ergodic Schrödinger operator with a strongly localised pure point spectrum. Particular attention is paid to operators with deterministic potentials (quasi-periodic ones and those generated by subshifts of finite type). Our approach relies on reducing the problem to obtaining exponential estimates for the eigenfunction correlator. This provides an effective route from localisation to the Area Law and allows for the identification of additional spectral estimates that need to be proven for various classes of ergodic operators. We realise this approach by using various localisation techniques, including dynamical localisation and the uniformly localised eigenfunction property for bounded and unbounded ergodic operators (e.g. the Maryland model), as well as a new method for obtaining the corresponding exponential bounds for Schrödinger operators generated by subshifts of finite type.
ER -