PreprintCC BY-NC-ND 4.0arXiv
Interchanging limits in the mutual information of two intervals separated by one site
Abstract
In the paper J. Phys. A: Math. Theor. 53 (2020), 345303, the limiting mutual information between two intervals separated by one lattice site in a free-fermion chain was evaluated. The calculation replaces the entropy function by a regularized version depending on ε>0, takes the block lengths to infinity, and only then lets ε tend to zero. We prove that the opposite order gives the same constant 2log2−1. Moreover, we show that the same limit is obtained whenever both block lengths tend to infinity and ε tends to zero simultaneously, with no restriction on their relative rates. In fact, the error caused by the regularization is bounded by (1+ε)log(1+ε)−εlogε, uniformly in both block lengths.
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BibTeX
@misc{bellavita2026interchanging,
title = {{Interchanging limits in the mutual information of two intervals separated by one site}},
author = {Carlo Bellavita and Jani A. Virtanen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08210},
eprint = {2609.08210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08210},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Interchanging limits in the mutual information of two intervals separated by one site
AU - Carlo Bellavita
AU - Jani A. Virtanen
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08210
UR - https://arxiv.org/abs/2609.08210
AB - In the paper J. Phys. A: Math. Theor. 53 (2020), 345303, the limiting mutual information between two intervals separated by one lattice site in a free-fermion chain was evaluated. The calculation replaces the entropy function by a regularized version depending on ε>0, takes the block lengths to infinity, and only then lets ε tend to zero. We prove that the opposite order gives the same constant 2log2−1. Moreover, we show that the same limit is obtained whenever both block lengths tend to infinity and ε tends to zero simultaneously, with no restriction on their relative rates. In fact, the error caused by the regularization is bounded by (1+ε)log(1+ε)−εlogε, uniformly in both block lengths.
ER -