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Pramana

Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions

Nandini Trivedi, P. J. H. Denteneer, Dariush Heidarian, Richard T. Scalettar

Published Jun 1, 2005• 6 citations
Publisher
DOI
10.1007/bf02704167

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We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Hubbard model with diagonal disorder (Anderson-Hubbard model) is investigated analytically and numerically in the limit of infinite spatial dimensions, i.e., within a dynamical mean-field theory, at half-filling. Numerical results are obtained for three different disorder distributions by employing quantum Monte Carlo techniques, which provide an explicit finite-temperature solution of the model in this limit. The magnetic phase diagram is constructed from the zeros of the inverse averaged staggered susceptibility. We find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A strong coupling anomaly, i.e., an increase of the N\'eel temperature for increasing disorder, is discovered. An explicit explanation is given, which shows that in the case of diagonal disorder this is a generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phases. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.

Physical review. B, Condensed matter•Apr 15, 1995•131 citations
The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical XY model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of the magnetic field is characterized by the frustration f. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent z, the correlation length exponent \ensuremath{\nu}, and the universal conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z\ensuremath{\approxeq}1, 1/\ensuremath{\nu}\ensuremath{\approxeq}1.5, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.52\ifmmode\pm\else\textpm\fi{}0.03, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.83\ifmmode\pm\else\textpm\fi{}0.06. The value of ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.27\ifmmode\pm\else\textpm\fi{}0.04 for the case f=0, and z=1.14\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.49\ifmmode\pm\else\textpm\fi{}0.04 for the case f=1/2.
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 present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Hubbard model with diagonal disorder (Anderson-Hubbard model) is investigated analytically and numerically in the limit of infinite spatial dimensions, i.e., within a dynamical mean-field theory, at half-filling. Numerical results are obtained for three different disorder distributions by employing quantum Monte Carlo techniques, which provide an explicit finite-temperature solution of the model in this limit. The magnetic phase diagram is constructed from the zeros of the inverse averaged staggered susceptibility. We find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A strong coupling anomaly, i.e., an increase of the N\'eel temperature for increasing disorder, is discovered. An explicit explanation is given, which shows that in the case of diagonal disorder this is a generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phases. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.