Physical review. B, Solid state

Classical Linear-Chain Hubbard Model: Metal-Insulator Transition

Robert A. Bari

Published May 15, 1973• 12 citations

Abstract

The linear-chain Hubbard model with nearest-neighbor hopping parameter $t$ is reexpressed in terms of pseudospin operators according to the Jordan-Wigner transformation. The resulting spin model is then treated classically. It is found that for a half-filled band there is a phase transition in the ground state as a function of $t$. The electrical conductivity is calculated and shown to vanish discontinuously at the critical value of $4t = U$ (Coulomb repulsion). A Josephson-type relation is obtained between the difference in azimuthal angles of adjacent spins and the potential difference between sites. It is also shown that a local magnetic moment exists in the insulating state. For the non-half-filled band, it is shown that the ground state is ferromagnetic for $4t < U$.

DOI: 10.1103/physrevb.7.4318

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METAL-INSULATOR TRANSITION IN THE HUBBARD MODEL

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Physical review. B, Solid state

Classical Linear-Chain Hubbard Model: Metal-Insulator Transition

Robert A. Bari

Published May 15, 1973• 12 citations

Publisher

Abstract

The linear-chain Hubbard model with nearest-neighbor hopping parameter

t

is reexpressed in terms of pseudospin operators according to the Jordan-Wigner transformation. The resulting spin model is then treated classically. It is found that for a half-filled band there is a phase transition in the ground state as a function of

t

. The electrical conductivity is calculated and shown to vanish discontinuously at the critical value of

4t = U

(Coulomb repulsion). A Josephson-type relation is obtained between the difference in azimuthal angles of adjacent spins and the potential difference between sites. It is also shown that a local magnetic moment exists in the insulating state. For the non-half-filled band, it is shown that the ground state is ferromagnetic for

4t < U

DOI: 10.1103/physrevb.7.4318

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METAL-INSULATOR TRANSITION IN THE HUBBARD MODEL

Arianna Montorsi, Mario Rasetti

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G. I. Japaridze, R. Hayn, P. Lombardo +1 more

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Hiroki Nakano, Yoshinori Takahashi

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arXiv:1608.06866Physical review. B./Physical review. BJul 12, 20174 citations

Phases and phase transitions in the half-filled t−t′ Hubbard chain

G. I. Japaridze, R. M. Noack, D. Baeriswyl +1 more

We study the quantum phase transition from an insulator to a metal realized at ${t}^{\ensuremath{'}}={t}_{c}^{\ensuremath{'}}>0.5t$ in the ground state of the half-filled Hubbard chain with both nearest-neighbor $(t)$ and next-nearest-neighbor $({t}^{\ensuremath{'}})$ hopping. The study is carried out using the bosonization approach and density-matrix renormalization-group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line ${t}_{c}^{\ensuremath{'}}(U,t)$. We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.We study the quantum phase transition from an insulator to a metal realized at ${t}^{\ensuremath{'}}={t}_{c}^{\ensuremath{'}}>0.5t$ in the ground state of the half-filled Hubbard chain with both nearest-neighbor $(t)$ and next-nearest-neighbor $({t}^{\ensuremath{'}})$ hopping. The study is carried out using the bosonization approach and density-matrix renormalization-group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line ${t}_{c}^{\ensuremath{'}}(U,t)$. We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.

Physical Review BSep 18, 200723 citations

The linear-chain Hubbard model with nearest-neighbor hopping parameter

t

t

. The electrical conductivity is calculated and shown to vanish discontinuously at the critical value of

4t = U

4t < U

U

, depending on the value of the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}$, the model shows three different versions of the ground-state phase diagram. For ${t}^{\ensuremath{'}}<{t}_{c}^{{*}^{\ensuremath{'}}}$, the ground-state phase diagram consists of the following three insulating phases: band insulator at

U<{U}_{c}

, ferroelectric insulator at

{U}_{c}<U<{U}_{s}

, and correlated (Mott) insulator at

U>{U}_{c}

. For ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ there is only one transition from a spin-gapped metallic phase at

U<{U}_{c}

to a ferroelectric insulator at

U>{U}_{c}

. Finally, for intermediate values of the next-nearest-neighbor hopping amplitude ${t}_{c}^{{*}^{\ensuremath{'}}}<{t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$ we find that with increasing on-site repulsion, at

{U}_{c1}

the model undergoes a second-order commensurate-incommensurate-type transition from a band insulator into a metallic state and at larger

{U}_{c2}

there is a Kosterlitz-Thouless-type transition from a metal to a ferroelectric insulator.

{t}_{2}

leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.

We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion

U

and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude

t

. We identify three different phases as functions of the disorder amplitude

W

and Coulomb interaction strength

U>0

. When

U<4t

the system shows a metallic phase: (i) only when no disorder is present

W=0

or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When

U>4t

the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.

(t)

and next-nearest-neighbor $({t}^{\ensuremath{'}})$ hopping. The study is carried out using the bosonization approach and density-matrix renormalization-group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line ${t}_{c}^{\ensuremath{'}}(U,t)$. We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.