arXiv:cond-mat/9609034 · Physical Review Letters

Quantum Transition between an Antiferromagnetic Mott Insulator and dx2−y2 Superconductor in Two Dimensions

Fakher F. Assaad, Masatoshi Imada, Douglas J. Scalapino

Published Nov 25, 1996• 55 citations

Abstract

We consider a Hubbard model on a square lattice with an additional interaction, $W$, which depends upon the square of the near-neighbor hopping. At half filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction $W$ drives the system from an antiferromagnetic Mott insulator to a ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to $16\ifmmode\times\else\texttimes\fi{}16$.

DOI: 10.1103/physrevlett.77.4592

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Charge and spin structures of a dx2−y2 superconductor in the proximity of an antiferromagnetic Mott insulator

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arXiv:cond-mat/9706173Physical review. B, Condensed matterDec 15, 199754 citations

t-U-Wmodel of a dx2−y2 superconductor in the proximity of an antiferromagnetic Mott insulator: Diagrammatic studies versus quantum Monte Carlo simulations

Thomas Eckl, Enrico Arrigoni, Werner R. Hanke +1 more

arXiv:cond-mat/0004171Physical review. B, Condensed matterNov 1, 20001 citation

Doping-induced metal-insulator transition in two-dimensional Hubbard t−U and extended Hubbard t−U−W models

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arXiv:cond-mat/9711172Physical review. B, Condensed matterJul 15, 199820 citations

Phase separation and competition of superconductivity and magnetism in the two-dimensional Hubbard model: From strong to weak coupling

Markus Aichhorn, Enrico Arrigoni, Michael Potthoff +1 more

arXiv:0707.3557Physical Review BDec 11, 200763 citations

Second-neighbor hopping in the attractive Hubbard model

Raimundo R. dos Santos

Physical review. B, Condensed matterSep 1, 199211 citations

Crossover between BCS Superconductor and Doped Mott Insulator of d -Wave Pairing State in Two-Dimensional Hubbard Model

Hisatoshi Yokoyama, Masao Ogata, Yukio Tanaka +2 more

arXiv:1208.1102Journal of the Physical Society of JapanJan 15, 2013100 citations

arXiv:cond-mat/9609034 · Physical Review Letters

Quantum Transition between an Antiferromagnetic Mott Insulator and dx2−y2 Superconductor in Two Dimensions

Fakher F. Assaad, Masatoshi Imada, Douglas J. Scalapino

Published Nov 25, 1996• 55 citations

arXiv HTML PDF

Abstract

We consider a Hubbard model on a square lattice with an additional interaction,

W

, which depends upon the square of the near-neighbor hopping. At half filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction

W

drives the system from an antiferromagnetic Mott insulator to a

{d}_{{x}^{2}{\ensuremath{-}y}^{2}}

superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to

16\ifmmode\times\else\texttimes\fi{}16

DOI: 10.1103/physrevlett.77.4592

Related papers

Charge and spin structures of a dx2−y2 superconductor in the proximity of an antiferromagnetic Mott insulator

Fakher F. Assaad, Masatoshi Imada, Douglas J. Scalapino

To the Hubbard model on a square lattice we add an interaction $W$ that depends upon the square of a near-neighbor hopping. We use zero-temperature quantum Monte Carlo simulations on lattice sizes up to $16\ifmmode\times\else\texttimes\fi{}16,$ to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor. With a combination of finite-temperature quantum Monte Carlo simulations and the maximum entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite-temperature Kosterlitz-Thouless transition to the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, ${T}_{\mathrm{KT}},$ we compute the one-electron density of states $N(\ensuremath{\omega}),$ the spin relaxation rate ${1/T}_{1},$ as well as the imaginary and real part of the spin susceptibility $\ensuremath{\chi}(q\ensuremath{\rightarrow},\ensuremath{\omega}).$ The spin dynamics are characterized by the vanishing of ${1/T}_{1}$ and divergence of $\mathrm{Re}\ensuremath{\chi}(q\ensuremath{\rightarrow}=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}=0)$ in the low-temperature limit. As ${T}_{\mathrm{KT}}$ is approached $N(\ensuremath{\omega})$ develops a pseudogap feature and below ${T}_{\mathrm{KT}}\mathrm{Im}\ensuremath{\chi}(q\ensuremath{\rightarrow}=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega})$ shows a peak at finite frequency.To the Hubbard model on a square lattice we add an interaction $W$ that depends upon the square of a near-neighbor hopping. We use zero-temperature quantum Monte Carlo simulations on lattice sizes up to $16\ifmmode\times\else\texttimes\fi{}16,$ to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor. With a combination of finite-temperature quantum Monte Carlo simulations and the maximum entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite-temperature Kosterlitz-Thouless transition to the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, ${T}_{\mathrm{KT}},$ we compute the one-electron density of states $N(\ensuremath{\omega}),$ the spin relaxation rate ${1/T}_{1},$ as well as the imaginary and real part of the spin susceptibility $\ensuremath{\chi}(q\ensuremath{\rightarrow},\ensuremath{\omega}).$ The spin dynamics are characterized by the vanishing of ${1/T}_{1}$ and divergence of $\mathrm{Re}\ensuremath{\chi}(q\ensuremath{\rightarrow}=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}=0)$ in the low-temperature limit. As ${T}_{\mathrm{KT}}$ is approached $N(\ensuremath{\omega})$ develops a pseudogap feature and below ${T}_{\mathrm{KT}}\mathrm{Im}\ensuremath{\chi}(q\ensuremath{\rightarrow}=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega})$ shows a peak at finite frequency.

arXiv:cond-mat/9706173Physical review. B, Condensed matterDec 15, 199754 citations

t-U-Wmodel of a dx2−y2 superconductor in the proximity of an antiferromagnetic Mott insulator: Diagrammatic studies versus quantum Monte Carlo simulations

Thomas Eckl, Enrico Arrigoni, Werner R. Hanke +1 more

We examine the competition and relationship between an antiferromagnetic (AF) Mott insulating state and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting (SC) state in two dimensions using semianalytical, i.e., diagrammatic calculations of the t-U-W model. The AF Mott insulator is described by the ground state of the half filled Hubbard model on a square lattice with on-site Coulomb repulsion U and nearest-neighbor single-particle hopping t. To this model, an extra term W is added, which depends upon the square of the single-particle nearest-neighbor hopping. Staying at half band filling and a constant value of U, it was previously shown with quantum Monte Carlo (QMC) simulations that one can generate a quantum transition as a function of the coupling strength W between an AF Mott insulating state and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\mathrm{SC}$ state. Here we complement these earlier QMC simulations with physically more transparent diagrammatic calculations. We start with a standard Hartree-Fock (HF) calculation to capture the ``high-energy'' physics of the t-U-W model. Then, we derive and solve the Bethe-Salpeter equation, i.e., we account for fluctuation effects within the time-dependent HF or generalized random-phase approximation scheme. Spin and charge susceptibility as well as the effective interaction vertex are calculated and systematically compared with QMC data. Finally, the corresponding BCS gap equation obtained for this effective interaction is solved.We examine the competition and relationship between an antiferromagnetic (AF) Mott insulating state and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting (SC) state in two dimensions using semianalytical, i.e., diagrammatic calculations of the t-U-W model. The AF Mott insulator is described by the ground state of the half filled Hubbard model on a square lattice with on-site Coulomb repulsion U and nearest-neighbor single-particle hopping t. To this model, an extra term W is added, which depends upon the square of the single-particle nearest-neighbor hopping. Staying at half band filling and a constant value of U, it was previously shown with quantum Monte Carlo (QMC) simulations that one can generate a quantum transition as a function of the coupling strength W between an AF Mott insulating state and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\mathrm{SC}$ state. Here we complement these earlier QMC simulations with physically more transparent diagrammatic calculations. We start with a standard Hartree-Fock (HF) calculation to capture the ``high-energy'' physics of the t-U-W model. Then, we derive and solve the Bethe-Salpeter equation, i.e., we account for fluctuation effects within the time-dependent HF or generalized random-phase approximation scheme. Spin and charge susceptibility as well as the effective interaction vertex are calculated and systematically compared with QMC data. Finally, the corresponding BCS gap equation obtained for this effective interaction is solved.

arXiv:cond-mat/0004171Physical review. B, Condensed matterNov 1, 20001 citation

Doping-induced metal-insulator transition in two-dimensional Hubbard t−U and extended Hubbard t−U−W models

Fakher F. Assaad, Masatoshi Imada

We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element $t$ and Coulomb repulsion $U$ is radically altered by the inclusion of a term $W$ that depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length ${\ensuremath{\xi}}_{l}$ in the insulating state. At $W/t=0.05$ and $U/t=4$ , we find results consistent with ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/2}$ where ${\ensuremath{\mu}}_{c}$ is the critical chemical potential. In contrast, ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/4}$ for the Hubbard model at $U/t=4$ . At half-filling, we calculate the density of states $N(\ensuremath{\omega})$. The large value of $N(\ensuremath{\omega})$ in the vicinity of $\ensuremath{\omega}={\ensuremath{\mu}}_{c}$ present at $W=0$ is suppressed with growing values of $W$ . At finite doping, the $d$ -wave pair-field correlations are enhanced with growing values of $W$ . The numerical results imply that at finite values of $W$ doping the antiferromagnetic Mott insulator leads to a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor.We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element $t$ and Coulomb repulsion $U$ is radically altered by the inclusion of a term $W$ that depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length ${\ensuremath{\xi}}_{l}$ in the insulating state. At $W/t=0.05$ and $U/t=4$, we find results consistent with ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/2}$ where ${\ensuremath{\mu}}_{c}$ is the critical chemical potential. In contrast, ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/4}$ for the Hubbard model at $U/t=4$. At half-filling, we calculate the density of states $N(\ensuremath{\omega})$. The large value of $N(\ensuremath{\omega})$ in the vicinity of $\ensuremath{\omega}={\ensuremath{\mu}}_{c}$ present at $W=0$ is suppressed with growing values of $W$. At finite doping, the $d$-wave pair-field correlations are enhanced with growing values of $W$. The numerical results imply that at finite values of $W$ doping the antiferromagnetic Mott insulator leads to a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor.

arXiv:cond-mat/9711172Physical review. B, Condensed matterJul 15, 199820 citations

Phase separation and competition of superconductivity and magnetism in the two-dimensional Hubbard model: From strong to weak coupling

Markus Aichhorn, Enrico Arrigoni, Michael Potthoff +1 more

Cooperation and competition between the antiferromagnetic, $d$ -wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength $U$ below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.Cooperation and competition between the antiferromagnetic, $d$-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength $U$ below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.

arXiv:0707.3557Physical Review BDec 11, 200763 citations

Second-neighbor hopping in the attractive Hubbard model

Raimundo R. dos Santos

We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor ( ${\mathit{t}}_{2}$ ) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert}, ${\mathit{t}}_{2}$ induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with ${\mathit{t}}_{2}$ .We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (${\mathit{t}}_{2}$) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert}, ${\mathit{t}}_{2}$ induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with ${\mathit{t}}_{2}$.

Physical review. B, Condensed matterSep 1, 199211 citations

Crossover between BCS Superconductor and Doped Mott Insulator of d -Wave Pairing State in Two-Dimensional Hubbard Model

Hisatoshi Yokoyama, Masao Ogata, Yukio Tanaka +2 more

With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of $U$ for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of $U$ for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.

arXiv:1208.1102Journal of the Physical Society of JapanJan 15, 2013100 citations

We consider a Hubbard model on a square lattice with an additional interaction,

W

, which depends upon the square of the near-neighbor hopping. At half filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction

W

drives the system from an antiferromagnetic Mott insulator to a

{d}_{{x}^{2}{\ensuremath{-}y}^{2}}

superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to

16\ifmmode\times\else\texttimes\fi{}16

To the Hubbard model on a square lattice we add an interaction

W

that depends upon the square of a near-neighbor hopping. We use zero-temperature quantum Monte Carlo simulations on lattice sizes up to $16\ifmmode\times\else\texttimes\fi{}16,$ to show that at half-filling and constant value of the Hubbard repulsion, the interaction

W

triggers a quantum transition between an antiferromagnetic Mott insulator and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor. With a combination of finite-temperature quantum Monte Carlo simulations and the maximum entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite-temperature Kosterlitz-Thouless transition to the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature,

{T}_{\mathrm{KT}},

we compute the one-electron density of states $N(\ensuremath{\omega}),$ the spin relaxation rate

{1/T}_{1},

as well as the imaginary and real part of the spin susceptibility $\ensuremath{\chi}(q\ensuremath{\rightarrow},\ensuremath{\omega}).$ The spin dynamics are characterized by the vanishing of

{1/T}_{1}

and divergence of $\mathrm{Re}\ensuremath{\chi}(q\ensuremath{\rightarrow}=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}=0)$ in the low-temperature limit. As

{T}_{\mathrm{KT}}

is approached $N(\ensuremath{\omega})$ develops a pseudogap feature and below ${T}_{\mathrm{KT}}\mathrm{Im}\ensuremath{\chi}(q\ensuremath{\rightarrow}=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega})$ shows a peak at finite frequency.

We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element

t

and Coulomb repulsion

U

is radically altered by the inclusion of a term

W

that depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length ${\ensuremath{\xi}}_{l}$ in the insulating state. At

W/t=0.05

and

U/t=4

, we find results consistent with ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/2}$ where ${\ensuremath{\mu}}_{c}$ is the critical chemical potential. In contrast, ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/4}$ for the Hubbard model at

U/t=4

. At half-filling, we calculate the density of states $N(\ensuremath{\omega})$. The large value of $N(\ensuremath{\omega})$ in the vicinity of $\ensuremath{\omega}={\ensuremath{\mu}}_{c}$ present at

W=0

is suppressed with growing values of

W

. At finite doping, the

d

-wave pair-field correlations are enhanced with growing values of

W

. The numerical results imply that at finite values of

W

doping the antiferromagnetic Mott insulator leads to a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor.

Cooperation and competition between the antiferromagnetic,

d

-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength

U

below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.

We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (

{\mathit{t}}_{2}

) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert},

{\mathit{t}}_{2}

induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with

{\mathit{t}}_{2}

U

for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.