Single-site diagonal quantities capture off-diagonal long-range order
Abstract
Quantum phase transitions are typically marked by changes in quantum correlations across various spatial scales within the system. A key challenge lies in the fact that experimental probes are generally restricted to diagonal quantities at the single-site scale, which are widely believed to be insufficient for detecting phases with off-diagonal long-range order, such as superconducting states. In a striking departure from conventional expectations, we show that single-site diagonal descriptors -- charge and spin fluctuations, occupation probabilities, and entanglement -- can capture the emergence of off-diagonal long-range order in the one-dimensional extended Hubbard model at half-filling. These single-site quantities display clear critical signatures of the superconducting transition, preceded by a continuous breaking of particle-hole symmetry, consistent with a second-order phase transition. While this symmetry breaking has a negligible effect on single-site descriptors, it allows a direct connection between local fluctuations and nonlocal correlations.
Cite
@article{arxiv.2507.10328,
title = {Single-site diagonal quantities capture off-diagonal long-range order},
author = {M. Sanino and I. D'Amico and V. V. França and I. M. Carvalho},
journal= {arXiv preprint arXiv:2507.10328},
year = {2025}
}