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arXiv:cond-mat/9609236 · Physical review. B, Condensed matter

Magnetic correlations in the two-dimensional Anderson-Hubbard model

M. Ulmke, Richard T. Scalettar

Published Feb 15, 1997• 42 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.55.4149

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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.
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.
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.
Anderson-Hubbard Model in d=∞d = \inftyd=∞
We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions at half filling. We construct the magnetic phase diagram and find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A novel strong coupling anomaly, i.e.~an {\it increase} of the Néel-temperature for increasing disorder, is discovered and explained as an generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phase. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.
Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to T=t20T=\frac{t}{20}T=20t​ (t=hoppingt=\mathrm{hopping}t=hopping) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion UUU. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.
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.