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arXiv:cond-mat/9707068 · Europhysics Letters (EPL)

Enhancement of long-range antiferromagnetic order by nonmagnetic impurities in the Hubbard model

M. Ulmke, P. J. H. Denteneer, Richard T. Scalettar, Gergely T. Zimányi

Published Jun 15, 1998• 13 citations
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Abstract

The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P ( U i ) = (1 − f )δ( U i − U ) + f δ( U i ), is studied using finite-temperature Quantum Monte Carlo and dynamical mean-field theory. Long-range antiferromagnetic order off half-filling is stabilized by the disorder, due to localization of the dopants on the U = 0 sites. Whereas in the clean model there is a single gap at n = 1, for nonzero f we find the compressibility and density of states exhibit gaps at two separate fillings.

DOI
10.1209/epl/i1998-00301-2

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Physical review. B, Condensed matter•Mar 1, 1987•185 citations
The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P ( U i ) = (1 − f )δ( U i − U ) + f δ( U i ), is studied using finite-temperature Quantum Monte Carlo and dynamical mean-field theory. Long-range antiferromagnetic order off half-filling is stabilized by the disorder, due to localization of the dopants on the U = 0 sites. Whereas in the clean model there is a single gap at n = 1, for nonzero f we find the compressibility and density of states exhibit gaps at two separate fillings.
The Hubbard model is studied in which disorder is introduced by putting the on-site interaction to zero on a fraction f of (impurity) sites of a square lattice. Using Quantum Monte Carlo methods and Dynamical Mean–Field Theory we find that antiferromagnetic long–range order is initially enhanced at half–filling and stabilized off half-filling by the disorder. The Mott-Hubbard charge gap of the pure system is broken up in two pieces by the disorder: one incompressible state remains at average density n = 1 and another can be seen slightly below n = 1 + f. Qualitative explanations are provided.
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.
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
We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two-dimensional, repulsive Hubbard model at T=0.T=0.T=0. A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, U<2tU<2tU<2t in the case of bond disorder, and U<4tU<4tU<4t in the case of on-site disorder. Using ground-state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For U=4t,U=4t,U=4t, we find a critical bond disorder of ${V}_{c}\ensuremath{\approx}(1.6\ifmmode\pm\else\textpm\fi{}0.4)t$ even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of ${V}_{c}\ensuremath{\approx}(5.0\ifmmode\pm\else\textpm\fi{}0.5)t$ at U=4t.U=4t.U=4t.
We study the effects of disorder on long range antiferromagnetic correlations and the Mott gap in the half-filled, two dimensional, repulsive Hubbard model. We employ Hartree-Fock (HF) and Quantum Monte Carlo (QMC) techniques in our study of the bond and site disordered models. Results from mean field (HF) calculations are used to develop a qualitative picture of the physics and to guide our choice for input to the QMC methods. The basic properties of two QMC methods for correlated fermions are discussed, and the results from these different approaches are presented.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.