Single-site diagonal quantities capture off-diagonal long-range order

TL;DR

This paper demonstrates that single-site diagonal quantities like charge and spin fluctuations can detect off-diagonal long-range order and superconducting transitions in a 1D extended Hubbard model, challenging conventional beliefs.

Contribution

It reveals that local diagonal descriptors can identify off-diagonal long-range order and phase transitions, providing new insights into quantum correlations.

Findings

Single-site descriptors show critical signatures of superconducting transition.

Particle-hole symmetry breaking precedes the phase transition.

Local fluctuations relate directly to nonlocal correlations.

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.