Derivation and numerical study of the singlet-triplet model for cuprate superconductors

Journal Article · Fri Sep 01 04:00:00 EDT 1995 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.52.7701· OSTI ID:115874

Simon, M E; Aligia, A A ^[1]

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1. International Centre for Theoretical Physics, Strada Costiera 11, P.O. Box 586, 34100 Trieste (Italy)

We perform a low-energy reduction of the three-band Hubbard Hamiltonian ({ital H}{sub 3{ital b}}), keeping in the relevant Hilbert subspace not only local singlets (Zhang-Rice singlets), but also triplet states between Cu holes and O holes at the Wannier function of the same site, with {ital x}{sup 2}-{ital y}{sup 2} symmetry. We solve exactly the resulting Hamiltonian {ital H}{sub {ital T}} in a system of 2{times}2 unit cells. From the analytical dependence of the parameters of {ital H}{sub {ital T}} and the numerical results, one can see that the local triplet states can be practically neglected for finite O-Cu on-site energy difference {Delta}, very large Cu on-site Coulomb repulsion {ital U}{sub {ital d}}, and O-O hopping {ital t}{sub {ital p}{ital p}}=0. This fact is in contrast with the mapping of {ital H}{sub 3{ital b}} to a one-band model using nonorthogonal singlets, which is very accurate when the Cu{sup +} configuration can be neglected. Although the amount of local triplet states in the low-energy eigenstates is in general small, it increases with {ital t}{sub {ital p}{ital p}} and for large {ital t}{sub {ital p}{ital p}} it is necessary to introduce higher-order corrections in the one-band model to accurately represent the low-energy physics. In all cases even when local triplets are not important, the {ital t}-{ital J} model should be supplemented with other terms, to describe the lowest-energy levels. We also discuss briefly the effect of nonbonding O orbitals.

• Sponsoring Organization: USDOE
• OSTI ID: 115874
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 10 Vol. 52; ISSN 0163-1829; ISSN PRBMDO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHEMICAL BONDS
COPPER
COULOMB FIELD
HAMILTONIANS
HIGH-TC SUPERCONDUCTORS
HUBBARD MODEL
NUMERICAL SOLUTION
OXYGEN