We perform a low-energy reduction of the three-band Hubbard Hamiltonian ( ${\mathit{H}}_{3\mathit{b}}$ ), 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 ${\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ symmetry. We solve exactly the resulting Hamiltonian ${\mathit{H}}_{\mathit{T}}$ in a system of 2\ifmmode\times\else\texttimes\fi{}2 unit cells. From the analytical dependence of the parameters of ${\mathit{H}}_{\mathit{T}}$ and the numerical results, one can see that the local triplet states can be practically neglected for finite O-Cu on-site energy difference \ensuremath{\Delta}, very large Cu on-site Coulomb repulsion ${\mathit{U}}_{\mathit{d}}$ , and O-O hopping ${\mathit{t}}_{\mathit{p}\mathit{p}}$ =0. This fact is in contrast with the mapping of ${\mathit{H}}_{3\mathit{b}}$ to a one-band model using nonorthogonal singlets, which is very accurate when the ${\mathrm{Cu}}^{+}$ configuration can be neglected. Although the amount of local triplet states in the low-energy eigenstates is in general small, it increases with ${\mathit{t}}_{\mathit{p}\mathit{p}}$ and for large ${\mathit{t}}_{\mathit{p}\mathit{p}}$ 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 t-J model should be supplemented with other terms, to describe the lowest-energy levels. We also discuss briefly the effect of nonbonding O orbitals.We perform a low-energy reduction of the three-band Hubbard Hamiltonian (${\mathit{H}}_{3\mathit{b}}$), 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 ${\mathit{x}}^{2}$-${\mathit{y}}^{2}$ symmetry. We solve exactly the resulting Hamiltonian ${\mathit{H}}_{\mathit{T}}$ in a system of 2\ifmmode\times\else\texttimes\fi{}2 unit cells. From the analytical dependence of the parameters of ${\mathit{H}}_{\mathit{T}}$ and the numerical results, one can see that the local triplet states can be practically neglected for finite O-Cu on-site energy difference \ensuremath{\Delta}, very large Cu on-site Coulomb repulsion ${\mathit{U}}_{\mathit{d}}$, and O-O hopping ${\mathit{t}}_{\mathit{p}\mathit{p}}$=0. This fact is in contrast with the mapping of ${\mathit{H}}_{3\mathit{b}}$ to a one-band model using nonorthogonal singlets, which is very accurate when the ${\mathrm{Cu}}^{+}$ configuration can be neglected. Although the amount of local triplet states in the low-energy eigenstates is in general small, it increases with ${\mathit{t}}_{\mathit{p}\mathit{p}}$ and for large ${\mathit{t}}_{\mathit{p}\mathit{p}}$ 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 t-J model should be supplemented with other terms, to describe the lowest-energy levels. We also discuss briefly the effect of nonbonding O orbitals.

Physical review. B, Condensed matterSep 1, 199525 citations

Recent Numerical Studies on Models for High-Tc Superconductors

Masatoshi Imada

Springer series in materials scienceJan 1, 19890 citations

Numerical investigations of models of the cuprates

Thomas Devereaux

Jan 20, 20211 citation

Hole excitation spectra in cuprate superconductors: A comparative study of single- and multiple-band strong-coupling theories

C.-H. Chen, H.-B. Schüttler, A. J. Fedro

We compare ground-state properties as well as spin and single-particle excitation spectra of a single dopant-induced hole carrier in strong-coupling-limit single-orbital and three-orbital Hubbard model lattices with up to 16 square lattice sites. Our results indicate that there is a close correspondence in their ground-state and low-lying excited-state properties, consistent with the recent proposal by Zhang and Rice (ZR). For the three-orbital model, we also find direct spectroscopic evidence for the singlet-triplet excitation gap associated with the dopant-induced ZR Cu-O spin-hole singlet state.We compare ground-state properties as well as spin and single-particle excitation spectra of a single dopant-induced hole carrier in strong-coupling-limit single-orbital and three-orbital Hubbard model lattices with up to 16 square lattice sites. Our results indicate that there is a close correspondence in their ground-state and low-lying excited-state properties, consistent with the recent proposal by Zhang and Rice (ZR). For the three-orbital model, we also find direct spectroscopic evidence for the singlet-triplet excitation gap associated with the dopant-induced ZR Cu-O spin-hole singlet state.

Physical review. B, Condensed matterFeb 1, 199043 citations

Coupling Spin Qubits via Superconductors

Martin Leijnse, Karsten Flensberg

We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two single-electron quantum dots are tunnel coupled to the same superconductor, the singlet component of the two-electron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gate-controlled singlet-triplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two double-dot singlet-triplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong two-qubit coupling over distances much larger than the coherence length.We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two single-electron quantum dots are tunnel coupled to the same superconductor, the singlet component of the two-electron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gate-controlled singlet-triplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two double-dot singlet-triplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong two-qubit coupling over distances much larger than the coherence length.

arXiv:1303.3507Physical Review LettersAug 6, 201353 citations

We perform a low-energy reduction of the three-band Hubbard Hamiltonian (

{\mathit{H}}_{3\mathit{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

{\mathit{x}}^{2}

{\mathit{y}}^{2}

symmetry. We solve exactly the resulting Hamiltonian

{\mathit{H}}_{\mathit{T}}

in a system of 2\ifmmode\times\else\texttimes\fi{}2 unit cells. From the analytical dependence of the parameters of

{\mathit{H}}_{\mathit{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 \ensuremath{\Delta}, very large Cu on-site Coulomb repulsion

{\mathit{U}}_{\mathit{d}}

, and O-O hopping

{\mathit{t}}_{\mathit{p}\mathit{p}}

=0. This fact is in contrast with the mapping of

{\mathit{H}}_{3\mathit{b}}

to a one-band model using nonorthogonal singlets, which is very accurate when the

{\mathrm{Cu}}^{+}

configuration can be neglected. Although the amount of local triplet states in the low-energy eigenstates is in general small, it increases with

{\mathit{t}}_{\mathit{p}\mathit{p}}

and for large

{\mathit{t}}_{\mathit{p}\mathit{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 t-J model should be supplemented with other terms, to describe the lowest-energy levels. We also discuss briefly the effect of nonbonding O orbitals.