Journal
PHYSICAL REVIEW B
Volume 105, Issue 11, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.105.115145
Keywords
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Funding
- FAPEMIG (Fundacao de Amparo a Pesquisa do Estado de Minas Gerais)
- CAPES (Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior)
- CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico)
- INCT-IQ (National Institute of Science and Technology for Quantum Information)
- National Council for Scientific and Technological Development-CNPq [308205/2019-7]
- FAPERJ [E26/211.318/2019]
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We studied the ground state properties of the one-dimensional extended Hubbard model at half filling from the perspective of its particle reduced density matrix. Our analysis of quantum correlations and coherence showed that different properties exhibit complementary behaviors and provide a qualitative view of the model's phase diagram. In particular, we found a transition in the entanglement spectrum signaling a change in the pairing ordering in the superconducting region.
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 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(i) 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 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 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 ground state wave function, not discussed previously in the literature. While other quantifiers are less sensitive to few-body defects in the wave function, the entanglement gap can work as a magnifying glass for these, capturing such small fluctuations.
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