arXiv:cond-mat/9704027

The Mott-Anderson transition in the disordered one-dimensional Hubbard model

Ramesh V. Pai, Alexander Punnoose, Rudolf A. Römer

Published Apr 3, 1997• 1 citation

Abstract

We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder $Δ_c \approx U/2$. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

DOI: 10.48550/arxiv.cond-mat/9704027

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arXiv:cond-mat/9704027

The Mott-Anderson transition in the disordered one-dimensional Hubbard model

Ramesh V. Pai, Alexander Punnoose, Rudolf A. Römer

Published Apr 3, 1997• 1 citation

arXiv HTML PDF

Abstract

Δ_c \approx U/2

. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

DOI: 10.48550/arxiv.cond-mat/9704027

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Δ_c \approx U/2

The one-dimensional

\mathrm{SU}(n)

Hubbard model is investigated numerically for

n=2

, 3, 4, and 5 at half-filling and

1∕n

filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive

U

n>2

. Furthermore, it is shown that the transition to the gapped phase at

{U}_{c}=0

is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd

n

. In the

1∕n

-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for

U>{U}_{c}=0

, the spin sector remains gapless, and the ground state is nondimerized.

{\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.

{\mathit{U}}_{\mathit{c}}

. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

U

reaches a critical value

U_c

. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

{U=U}_{c}

and

{U=U}_{s}

that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase

(U<{U}_{c})

and drops below the band gap when U exceeds a special point

{U}_{e}.

The exciton gap closes at the first critical point

{U}_{c}

while the charge and spin gaps persist and coincide between

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

where the system is dimerized. Both the charge and spin gaps collapse at

{U=U}_{s}

when the transition to the MI phase occurs. In the MI phase

(U>{U}_{s})

the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.