Quantum correlations, entanglement spectrum, and coherence of the twoparticle reduced density matrix in the extended Hubbard model
Abstract
We study the ground state properties of the onedimensional extended Hubbard model at half filling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of two 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) ℓ_{1} norm of coherence, (iii) irreducible twobody 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 and 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 from 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 SSTS 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 fewbody level—in the ground state wave function, not discussed previously in the literature. While other quantifiers are less sensitive to fewbody defects in the wave function, the entanglement gap can work as a magnifying glass for these, capturing such small fluctuations.
 Publication:

Physical Review B
 Pub Date:
 March 2022
 DOI:
 10.1103/PhysRevB.105.115145
 arXiv:
 arXiv:2111.00085
 Bibcode:
 2022PhRvB.105k5145F
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 14 pages and 7 figures