Physical Review Letters

New Phases in an Extended Hubbard Model Explicitly Including Atomic Polarizabilities

Jeroen van den Brink, M.B.J. Meinders, J. Lorenzana, R. Eder, G. A. Sawatzky

Published Dec 18, 1995• 55 citations

Abstract

We consider the influence of a nearest-neighbor Coulomb interaction in an extended Hubbard model and introduce a new interaction term which simulates atomic polarizabilities. This has the effect of screening the on-site Coulomb interaction for charged excitations, unlike a neighbor Coulomb interaction which reduces energies of locally neutral excitations. We find that the spin density to charge density wave phase transition, however, is determined by the unscreened on-site Coulomb repulsion. The order of this phase transition is affected by polarization. We show that new phases appear, one of which is ferroelectric, when atomic polarizabilities are explicitly included.

DOI: 10.1103/physrevlett.75.4658

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Physical Review Letters

New Phases in an Extended Hubbard Model Explicitly Including Atomic Polarizabilities

Jeroen van den Brink, M.B.J. Meinders, J. Lorenzana, R. Eder, G. A. Sawatzky

Published Dec 18, 1995• 55 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.75.4658

Related papers

Atomic screening and intersite Coulomb repulsion in strongly correlated systems

M.B.J. Meinders, Jeroen van den Brink, J. Lorenzana +1 more

We consider the influence of a nearest-neighbor Coulomb interaction in an extended Hubbard model and introduce an interaction term which simulates atomic polarizabilities. The inclusion of atomic polarizabilities in the model has the effect of screening the on-site Coulomb interaction for charged excitations, unlike a neighbor Coulomb interaction which reduces energies of neutral local excitations, leaving the conductivity gap unchanged. This is supported by an exact diagonalization study on small, mainly one-dimensional, extended Mott-Hubbard systems. For large V, the system undergoes a phase transition from a spin-density wave (SDW) to a charge-density wave (CDW). It is shown that the SDW/CDW phase transition cannot be described correctly when using effective parameters, but that screening effects have to be included explicitly. Also other phases, one of which is ferroelectric, appear when atomic polarizabilities are included in the model Hamiltonian. We study ${\mathrm{C}}_{60}$ in terms of the degenerate extended Hubbard model with screening effects.We consider the influence of a nearest-neighbor Coulomb interaction in an extended Hubbard model and introduce an interaction term which simulates atomic polarizabilities. The inclusion of atomic polarizabilities in the model has the effect of screening the on-site Coulomb interaction for charged excitations, unlike a neighbor Coulomb interaction which reduces energies of neutral local excitations, leaving the conductivity gap unchanged. This is supported by an exact diagonalization study on small, mainly one-dimensional, extended Mott-Hubbard systems. For large V, the system undergoes a phase transition from a spin-density wave (SDW) to a charge-density wave (CDW). It is shown that the SDW/CDW phase transition cannot be described correctly when using effective parameters, but that screening effects have to be included explicitly. Also other phases, one of which is ferroelectric, appear when atomic polarizabilities are included in the model Hamiltonian. We study ${\mathrm{C}}_{60}$ in terms of the degenerate extended Hubbard model with screening effects.

Physical review. B, Condensed matterJul 15, 199527 citations

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Quantum information analysis of the phase diagram of the half-filled extended Hubbard model

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We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.

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Computer renormalization-group calculations of the 2kF and 4kF correlation functions of an extended one-dimensional Hubbard model

S. T. Chui, J. W. Bray

We extend previous calculations of the $2{k}_{F}$ and $4{k}_{F}$ (${k}_{F}\ensuremath{\equiv}\mathrm{Fermi}\mathrm{wave}\mathrm{vector}$) spin- and charge-density autocorrelation functions of the one-dimensional Hubbard model by including the nearest-neighbor Coulomb interaction $V$ . The results are computed for finite chains containing up to eight sites using a computer renormalization-group technique previously developed by us. We find, inter alia, that the real part of the $4{k}_{F}$ charge-density wave (CDW), which is comparable to the real part of the $2{k}_{F}$ CDW when only large onsite Coulomb repulsion is considered, becomes greatly enhanced relative to the $2{k}_{F}$ CDW when $V$ is positive. This finding implies that the $V$ interaction is important in explaining the $4{k}_{F}$ instability of some quasi-one-dimensional materials.We extend previous calculations of the $2{k}_{F}$ and $4{k}_{F}$ (${k}_{F}\ensuremath{\equiv}\mathrm{Fermi}\mathrm{wave}\mathrm{vector}$) spin- and charge-density autocorrelation functions of the one-dimensional Hubbard model by including the nearest-neighbor Coulomb interaction $V$. The results are computed for finite chains containing up to eight sites using a computer renormalization-group technique previously developed by us. We find, inter alia, that the real part of the $4{k}_{F}$ charge-density wave (CDW), which is comparable to the real part of the $2{k}_{F}$ CDW when only large onsite Coulomb repulsion is considered, becomes greatly enhanced relative to the $2{k}_{F}$ CDW when $V$ is positive. This finding implies that the $V$ interaction is important in explaining the $4{k}_{F}$ instability of some quasi-one-dimensional materials.

Physical review. B, Condensed matterFeb 15, 198020 citations

Charge-Density-Wave to Spin-Density-Wave Transition in the Extended Hubbard Model

J. E. Hirsch

Monte Carlo simulations are used to study the charge-density-wave to spin-density-wave transition in the one-dimensional Hubbard model with on-site ( $U$ ) and nearest-neighbor ( $V$ ) repulsion. The transition is found to be continuous for small $U$ and first order for large $U$ , with the crossover occurring around $U\ensuremath{\sim}3$. The transition line deviates somewhat from the theoretical prediction $U=2V$ towards the charge-density-wave phase for intermediate coupling. A qualitative explanation for the results is given by use of strong-coupling arguments.Monte Carlo simulations are used to study the charge-density-wave to spin-density-wave transition in the one-dimensional Hubbard model with on-site ($U$) and nearest-neighbor ($V$) repulsion. The transition is found to be continuous for small $U$ and first order for large $U$, with the crossover occurring around $U\ensuremath{\sim}3$. The transition line deviates somewhat from the theoretical prediction $U=2V$ towards the charge-density-wave phase for intermediate coupling. A qualitative explanation for the results is given by use of strong-coupling arguments.

Physical Review LettersDec 10, 1984245 citations

{\mathrm{C}}_{60}

in terms of the degenerate extended Hubbard model with screening effects.

t=0

there are two charge density-wave phases, one spin density-wave phase, and one intermediate phase with charge and spin ordering, depending on the parameter values. At $t\ensuremath{\ne}0$ the nature of each phase is confirmed by studying correlation functions. However, in addition to the strong-coupling phases, a small region with bond ordering appears. The region occupied by the intermediate phase first increases and then decreases with increasing t, until it finally disappears for t of the order but larger than U. For small t, the topological transitions agree with the results of second-order perturbation theory.

We extend previous calculations of the

2{k}_{F}

and

4{k}_{F}

(${k}_{F}\ensuremath{\equiv}\mathrm{Fermi}\mathrm{wave}\mathrm{vector}$) spin- and charge-density autocorrelation functions of the one-dimensional Hubbard model by including the nearest-neighbor Coulomb interaction

V

. The results are computed for finite chains containing up to eight sites using a computer renormalization-group technique previously developed by us. We find, inter alia, that the real part of the

4{k}_{F}

charge-density wave (CDW), which is comparable to the real part of the

2{k}_{F}

CDW when only large onsite Coulomb repulsion is considered, becomes greatly enhanced relative to the

2{k}_{F}

CDW when

V

is positive. This finding implies that the

V

interaction is important in explaining the

4{k}_{F}

instability of some quasi-one-dimensional materials.

Monte Carlo simulations are used to study the charge-density-wave to spin-density-wave transition in the one-dimensional Hubbard model with on-site (

U

) and nearest-neighbor (

V

) repulsion. The transition is found to be continuous for small

U

and first order for large

U

, with the crossover occurring around $U\ensuremath{\sim}3$. The transition line deviates somewhat from the theoretical prediction

U=2V

towards the charge-density-wave phase for intermediate coupling. A qualitative explanation for the results is given by use of strong-coupling arguments.