Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model

TL;DR

This paper investigates the quantum correlations, coherence, and entanglement spectrum of the two-particle reduced density matrix in the one-dimensional extended Hubbard model, revealing phase-dependent behaviors and transitions, especially between singlet and triplet pairings.

Contribution

It provides a detailed analysis of the two-particle reduced density matrix, uncovering how various quantum properties signal phase transitions and pairing order changes in the extended Hubbard model.

Findings

Entanglement spectrum signals singlet-triplet transition.

Quantum correlations exhibit discontinuities at phase transitions.

Entanglement gap reveals subtle few-body ground state changes.

Abstract

We study the ground state properties of the one-dimensional extended Hubbard model at half-filling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of $2$ fermions and perform an analysis of its quantum correlations and coherence along the different phases of the model. Specifically, we study its (i) entanglement entropy, (ii) $\ell_1$ norm of coherence, (iii) irreducible two-body cumulant matrix and (iv) entanglement spectrum. Our results show that these different properties are complementary to each other depending on the phase of the system, exhibiting peculiar behaviors such as discontinuities, maximum or minimum values at the quantum phase transitions, thus providing a qualitative view of the phase diagram of the model. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system. Moreover, from the analysis of the dominant eigenvector in the reduced state, we can relate the SS-TS transition to the spatial separation between the fermion pairs in the two different pairing orderings. The entanglement gap is also able to highlight a transition - at a few-body level - in the groundstate wavefunction, not discussed previously in the literature. While other quantifiers are less sensitive to few-body defects in the wavefunction, the entanglement gap can work as a magnifying glass for these, capturing such small fluctuations.