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Physical review. B, Condensed matter

Effects of weak random disorder in the one-dimensional Hubbard model

Anders W. Sandvik, Douglas J. Scalapino

Published Apr 15, 1993• 11 citations
Publisher

Abstract

We introduce the notion of an impurity susceptibility as a measure of the effect of disorder on the properties of interacting many-particle systems. If finite, the impurity susceptibility gives the lowest-order correction to a given physical observable in the presence of disorder. If divergent, it signals that arbitrarily weak disorder leads to a qualitatively different physical behavior. Using a quantum Monte Carlo technique, impurity susceptibilities for various properties of the one-dimensional Hubbard model are calculated. Two types of disorder are considered; random hopping matrix elements and random potentials. For the local magnetic moment and the kinetic energy the impurity susceptibilities are finite. The impurity susceptibility of the q=2${\mathit{k}}_{\mathit{F}}$ spin response is divergent for both types of disorder, indicating a quenching of the T\ensuremath{\rightarrow}0 divergence of this quantity. The susceptibility of the q=0 spin response to random hopping diverges at half filling, as a consequence of a divergent magnetic susceptibility in the presence of this type of disorder. We also find large, possibly divergent, impurity susceptibilities for the q=2${\mathit{k}}_{\mathit{F}}$ and 4${\mathit{k}}_{\mathit{F}}$ charge-density responses.

DOI
10.1103/physrevb.47.10090

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Physical review. B, Condensed matter•Aug 1, 1993•39 citations
We introduce the notion of an impurity susceptibility as a measure of the effect of disorder on the properties of interacting many-particle systems. If finite, the impurity susceptibility gives the lowest-order correction to a given physical observable in the presence of disorder. If divergent, it signals that arbitrarily weak disorder leads to a qualitatively different physical behavior. Using a quantum Monte Carlo technique, impurity susceptibilities for various properties of the one-dimensional Hubbard model are calculated. Two types of disorder are considered; random hopping matrix elements and random potentials. For the local magnetic moment and the kinetic energy the impurity susceptibilities are finite. The impurity susceptibility of the q=2kF{\mathit{k}}_{\mathit{F}}kF​ spin response is divergent for both types of disorder, indicating a quenching of the T\ensuremath{\rightarrow}0 divergence of this quantity. The susceptibility of the q=0 spin response to random hopping diverges at half filling, as a consequence of a divergent magnetic susceptibility in the presence of this type of disorder. We also find large, possibly divergent, impurity susceptibilities for the q=2kF{\mathit{k}}_{\mathit{F}}kF​ and 4kF{\mathit{k}}_{\mathit{F}}kF​ charge-density responses.
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=2kF{\mathit{k}}_{\mathit{F}}kF​ 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.
The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced
We study the influence of disorder and randomly distributed impurities on the properties of band-antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed. 1
The two-dimensional Hubbard model in the presence of diagonal and off-diagonal disorder is studied at half-filling with a finite-temperature quantum Monte Carlo method. Magnetic correlations as well as the electronic compressibility are calculated to determine the behavior of local magnetic moments, the stability of antiferromagnetic long-range order (AFLRO), and properties of the disordered phase. The existence of random potentials (diagonal or ``site'' disorder) leads to a suppression of local magnetic moments which eventually destroys AFLRO. Randomness in the hopping elements (off-diagonal disorder), on the other hand, does not significantly reduce the density of local magnetic moments. For this type of disorder, at half-filling, there is no ``sign problem'' in the simulations as long as the hopping is restricted between neighbor sites on a bipartite lattice. This allows the study of sufficiently large lattices and low temperatures to perform a finite-size scaling analysis. For off-diagonal disorder, AFLRO is eventually destroyed when the fluctuations of antiferromagnetic exchange couplings exceed a critical value. The disordered phase close to the transition appears to be incompressible, and shows an increase of the uniform susceptibility at low temperatures.
An Anderson impurity in a Hubbard model on chains with finite length is studied using the density-matrix renormalization-group (DMRG) technique. In the first place, we analyzed how the reduction of electron density from half filling to quarter filling affects the Kondo resonance in the limit of Hubbard repulsion U=0U=0U=0. In general, a weak dependence with the electron density was found for the local density of states (LDOS), at the impurity except when the impurity, at half filling, is close to a mixed-valence regime. Next, in the central part of this paper, we studied the effects of finite Hubbard interaction on the chain at quarter filling. Our main result is that this interaction drives the impurity into a more defined Kondo regime although accompanied in most cases by a reduction of the spectral weight of the impurity LDOS. Again, for the impurity in the mixed-valence regime, we observed an interesting nonmonotonic behavior. We also concluded that the conductance, computed for a small finite bias applied to the leads, follows the behavior of the impurity LDOS, as in the case of noninteracting chains. Finally, we analyzed how the Hubbard interaction and the finite chain length affect the spin compensation cloud both at zero and at finite temperature, in this case using quantum Monte Carlo techniques.
Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.