arXiv:cond-mat/9310076 · Physical review. B, Condensed matter

Metal-insulator transition and magnetic ordering in Hubbard models near the Nagaoka limit

Q. P. Li, Robert Joynt

Published Jan 15, 1994• 10 citations

Abstract

We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. The analysis simplifies near the ferromagnetic limit. We find that the two-dimensional Hubbard model has a charge excitation gap at half filling for any finite U in this region on both the bipartite square lattice and the nonbipartite triangular lattice. In some cases, the system goes through a first-order phase transition to become a paramagnetic metal as ${\mathit{S}}_{\mathit{z}}$ is lowered. We also discuss the extension to the doped case. We find that in the large U limit, a single doped hole has a bandwidth of order of J rather than t at ${\mathit{S}}_{\mathit{z}}$=0.

DOI: 10.1103/physrevb.49.1632

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arXiv:cond-mat/9310076 · Physical review. B, Condensed matter

Metal-insulator transition and magnetic ordering in Hubbard models near the Nagaoka limit

Q. P. Li, Robert Joynt

Published Jan 15, 1994• 10 citations

arXiv HTML PDF

Abstract

{\mathit{S}}_{\mathit{z}}

is lowered. We also discuss the extension to the doped case. We find that in the large U limit, a single doped hole has a bandwidth of order of J rather than t at

{\mathit{S}}_{\mathit{z}}

=0.

DOI: 10.1103/physrevb.49.1632

Related papers

Mott-Hubbard metal-insulator transition in Hubbard models at high total spin

Q. P. Li, Robert Joynt

We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. This representation facilitates the exact solution of the half-filled band in the limit of high spin. We find that the two-dimensional Hubbard model has a charge-excitation gap at half filling for any finite U in the high-spin region on both the bipartite square lattice and the nonbipartite triangular lattice. We show, using the Kohn insulator criteria, that this bound-state phase is indeed insulating. Using the information from the single-pair solution, we construct a generalized BCS type of many-body wave function and derive the gap equation for lower-spin states. We find that in some cases, the system goes through a phase transition to become a metal as the total spin ${\mathit{S}}_{\mathit{z}}$ is lowered.We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. This representation facilitates the exact solution of the half-filled band in the limit of high spin. We find that the two-dimensional Hubbard model has a charge-excitation gap at half filling for any finite U in the high-spin region on both the bipartite square lattice and the nonbipartite triangular lattice. We show, using the Kohn insulator criteria, that this bound-state phase is indeed insulating. Using the information from the single-pair solution, we construct a generalized BCS type of many-body wave function and derive the gap equation for lower-spin states. We find that in some cases, the system goes through a phase transition to become a metal as the total spin ${\mathit{S}}_{\mathit{z}}$ is lowered.

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Mott metal-insulator transition in the half-filled Hubbard model on the triangular lattice

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We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.

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Journal of the Physical Society of JapanJan 15, 19984 citations

Anomalous paramagnetic phase of the Hubbard model

Takuya Okabe

A strong-coupling regime of the Hubbard model around half filling is investigated in the Hartree-Fock random-phase approximation. At half filling, besides a normal solution that gives rise to antiferromagnetic instability at ${T=T}_{\mathrm{N}}^{\mathrm{RPA}}\ensuremath{\sim}U,$ we find a solution representing the paramagnetic phase of the Mott insulator, for which we obtain the N\'eel temperature ${T}_{\mathrm{N}}\ensuremath{\sim}J$ in three-dimensional lattices. The solution is interpreted as the ferromagnetic band insulator depolarized by spin wave, the bound state of a particle-hole pair. Similarly, an anomalous metallic phase is derived from the Nagaoka ferromagnetic state. We evaluate ${T}_{\mathrm{N}}$ as a function of doping concentration x to find that it vanishes at $x\ensuremath{\simeq}0.05$ for $U/6t=4$ in a simple cubic lattice.A strong-coupling regime of the Hubbard model around half filling is investigated in the Hartree-Fock random-phase approximation. At half filling, besides a normal solution that gives rise to antiferromagnetic instability at ${T=T}_{\mathrm{N}}^{\mathrm{RPA}}\ensuremath{\sim}U,$ we find a solution representing the paramagnetic phase of the Mott insulator, for which we obtain the N\'eel temperature ${T}_{\mathrm{N}}\ensuremath{\sim}J$ in three-dimensional lattices. The solution is interpreted as the ferromagnetic band insulator depolarized by spin wave, the bound state of a particle-hole pair. Similarly, an anomalous metallic phase is derived from the Nagaoka ferromagnetic state. We evaluate ${T}_{\mathrm{N}}$ as a function of doping concentration x to find that it vanishes at $x\ensuremath{\simeq}0.05$ for $U/6t=4$ in a simple cubic lattice.

Physical review. B, Condensed matterJan 15, 19990 citations

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Phase diagram of the Hubbard model on a square lattice: A cluster slave-spin study

Minghuan Zeng, Tianxing Ma, Y.-J. Wang

The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\ensuremath{\delta}$ and coupling strength $U$ being its parameters. At half-filling, a relation between the staggered magnetization $M$ and the antiferromagnetic (AFM) gap ${\mathrm{\ensuremath{\Delta}}}_{\text{AFM}}$ is established in the small $U$ limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at ${U}_{\text{Mott}}=10t$ . The interaction ${U}_{c}$ for the crossover in the AFM state, separating the weak- and strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than ${U}_{\text{Mott}}$ at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the $U\ensuremath{-}\ensuremath{\delta}$ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility $\ensuremath{\kappa}>0$ or $\ensuremath{\kappa}<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative $\ensuremath{\kappa}$, and (iii) separating the AFM insulating phase at $\ensuremath{\delta}=0$ from the AFM metal phase for $\ensuremath{\delta}>0$.The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\ensuremath{\delta}$ and coupling strength $U$ being its parameters. At half-filling, a relation between the staggered magnetization $M$ and the antiferromagnetic (AFM) gap ${\mathrm{\ensuremath{\Delta}}}_{\text{AFM}}$ is established in the small $U$ limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at ${U}_{\text{Mott}}=10t$. The interaction ${U}_{c}$ for the crossover in the AFM state, separating the weak- and strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than ${U}_{\text{Mott}}$ at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the $U\ensuremath{-}\ensuremath{\delta}$ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility $\ensuremath{\kappa}>0$ or $\ensuremath{\kappa}<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative $\ensuremath{\kappa}$, and (iii) separating the AFM insulating phase at $\ensuremath{\delta}=0$ from the AFM metal phase for $\ensuremath{\delta}>0$.

arXiv:2106.05457Physical review. B./Physical review. BSep 29, 20215 citations

{\mathit{S}}_{\mathit{z}}

is lowered. We also discuss the extension to the doped case. We find that in the large U limit, a single doped hole has a bandwidth of order of J rather than t at

{\mathit{S}}_{\mathit{z}}

=0.

{\mathit{S}}_{\mathit{z}}

is lowered.

{T}_{\mathrm{N}}

as a function of doping concentration x to find that it vanishes at $x\ensuremath{\simeq}0.05$ for

U/6t=4

in a simple cubic lattice.

The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\ensuremath{\delta}$ and coupling strength

U

being its parameters. At half-filling, a relation between the staggered magnetization

M

and the antiferromagnetic (AFM) gap ${\mathrm{\ensuremath{\Delta}}}_{\text{AFM}}$ is established in the small

U

limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at

{U}_{\text{Mott}}=10t

. The interaction

{U}_{c}

for the crossover in the AFM state, separating the weak- and strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than

{U}_{\text{Mott}}

at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the $U\ensuremath{-}\ensuremath{\delta}$ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility $\ensuremath{\kappa}>0$ or $\ensuremath{\kappa}<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative $\ensuremath{\kappa}$, and (iii) separating the AFM insulating phase at $\ensuremath{\delta}=0$ from the AFM metal phase for $\ensuremath{\delta}>0$.