Physical review. B, Condensed matter

Single-particle hopping probability on a chain with interaction and disorder by the modified Lanczos algorithm

Cristina Wiecko, G. Chiappe

Published Jan 15, 1992• 1 citation

Abstract

We consider numerically a chain of ten sites (half filled) described by the Anderson-Hubbard model. The single-particle hopping probability is calculated as a function of disorder and correlation. A qualitative agreement for the logarithm of this hopping probability is found when compared with results of a calculation of the low-frequency conductivity by the Monte Carlo method.

DOI: 10.1103/physrevb.45.1900

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Physical review. B, Condensed matter

Single-particle hopping probability on a chain with interaction and disorder by the modified Lanczos algorithm

Cristina Wiecko, G. Chiappe

Published Jan 15, 1992• 1 citation

Publisher

Abstract

DOI: 10.1103/physrevb.45.1900

Related papers

Modified Lanczos simulation of the localized superconductivity for a chain with interaction and disorder

Cristina Wiecko, G. Chiappe

Physical review. B, Condensed matterDec 1, 19893 citations

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Francesca Battista, Alberto Camjayi, Liliana Arrachea

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.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.

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We have studied the effects of random-hopping matrix elements and random potentials on the properties of the one-dimensional Hubbard model. Using a quantum Monte Carlo technique, disorder-averaged static spin- and charge-density susceptiblities have been evaluated for various strengths of the disorder. Results for the spin susceptibility at wave number q=2 ${\mathit{k}}_{\mathit{F}}$ indicate that this quantity, which is the fastest diverging susceptibility of the pure system, diverges as T\ensuremath{\rightarrow}0 also when there is randomness in the hopping matrix elements, but not in the presence of random potentials. Both types of disorder cause a divergence of the uniform magnetic susceptibility. However, for random potentials a finite critical strength of the disorder appears to be required. At half-filling the transition from Mott (gapped) to Anderson (gapless) insulating behavior has been studied. A critical disorder strength is needed to destroy the gap, in agreement with Ma's renormalization group calculations.We have studied the effects of random-hopping matrix elements and random potentials on the properties of the one-dimensional Hubbard model. Using a quantum Monte Carlo technique, disorder-averaged static spin- and charge-density susceptiblities have been evaluated for various strengths of the disorder. Results for the spin susceptibility at wave number q=2${\mathit{k}}_{\mathit{F}}$ indicate that this quantity, which is the fastest diverging susceptibility of the pure system, diverges as T\ensuremath{\rightarrow}0 also when there is randomness in the hopping matrix elements, but not in the presence of random potentials. Both types of disorder cause a divergence of the uniform magnetic susceptibility. However, for random potentials a finite critical strength of the disorder appears to be required. At half-filling the transition from Mott (gapped) to Anderson (gapless) insulating behavior has been studied. A critical disorder strength is needed to destroy the gap, in agreement with Ma's renormalization group calculations.

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K. L. Liu, B. Bergersen

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Density-matrix renormalization-group studies of the alternating Hubbard model

Hanbin Pang, Shoudan Liang

Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.

Physical review. B, Condensed matterApr 15, 199520 citations

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.

{\mathrm{t}}_{\mathrm{AA}}

{\mathrm{t}}_{\mathrm{AB}}

{\mathrm{t}}_{\mathrm{BB}}

for ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$=0,1,2, respectively. For 0

{\mathrm{t}}_{\mathrm{AB}}

{\mathrm{t}}_{\mathrm{AA}}

{\mathrm{t}}_{\mathrm{BB}}

, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of

{\mathrm{t}}_{\mathrm{AB}}

=0. For 0

{\mathrm{t}}_{\mathrm{AB}}

{\mathrm{t}}_{\mathrm{AA}}

{\mathrm{t}}_{\mathrm{BB}}

, the GS is a M for sufficiently low values of U and V. In contrast, when

{\mathrm{t}}_{\mathrm{AA}}

{\mathrm{t}}_{\mathrm{BB}}

{2\mathrm{t}}_{\mathrm{AB}}

=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.

{\mathit{k}}_{\mathit{F}}

indicate that this quantity, which is the fastest diverging susceptibility of the pure system, diverges as T\ensuremath{\rightarrow}0 also when there is randomness in the hopping matrix elements, but not in the presence of random potentials. Both types of disorder cause a divergence of the uniform magnetic susceptibility. However, for random potentials a finite critical strength of the disorder appears to be required. At half-filling the transition from Mott (gapped) to Anderson (gapless) insulating behavior has been studied. A critical disorder strength is needed to destroy the gap, in agreement with Ma's renormalization group calculations.