34 research outputs found
Collective excitation spectrum of a disordered Hubbard model
We study the collective excitation spectrum of a d=3 site-disordered
Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA)
about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground
states. We focus in particular on the density and character of low-frequency
collective excitations in the transverse spin channel. In the absence of
disorder, these are found to be spin-wave-like for all but very weak
interaction strengths, extending down to zero frequency and separated from a
Stoner-like band, to which there is a gap. With disorder present, a prominent
spin-wave-like band is found to persist over a wide region of the
disorder-interaction phase plane in which the mean-field ground state is a
disordered antiferromagnet, despite the closure of the UHF single-particle gap.
Site resolution of the RPA excitations leads to a microscopic rationalization
of the evolution of the spectrum with disorder and interaction strength, and
enables the observed localization properties to be interpreted in terms of the
fraction of strong local moments and their site-differential distribution.Comment: 25 pages (revtex), 9 postscript figure
Insulating phases of the infinite-dimensional Hubbard model
A theory is developed for the T=0 Mott-Hubbard insulating phases of the
infinite-dimensional Hubbard model at half-filling, including both the
antiferromagnetic (AF) and paramagnetic (P) insulators. Local moments are
introduced explicitly from the outset, enabling ready identification of the
dominant low energy scales for insulating spin- flip excitations. Dynamical
coupling of single-particle processes to the spin-flip excitations leads to a
renormalized self-consistent description of the single-particle propagators
that is shown to be asymptotically exact in strong coupling, for both the AF
and P phases. For the AF case, the resultant theory is applicable over the
entire U-range, and is discussed in some detail. For the P phase, we consider
in particular the destruction of the Mott insulator, the resultant critical
behaviour of which is found to stem inherently from proper inclusion of the
spin-flip excitations.Comment: 13 pages Revtex, 12 postscript figure
Disorder and Impurities in Hubbard-Antiferromagnets
We study the influence of disorder and randomly distributed impurities on the
properties of correlated 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.Comment: 16 pages, 9 figures, latex using vieweg.sty (enclosed); typos
corrected, references updated; to appear in "Advances in Solid State
Physics", Vol. 3
Correlated electrons in the presence of disorder
Several new aspects of the subtle interplay between electronic correlations
and disorder are reviewed. First, the dynamical mean-field theory
(DMFT)together with the geometrically averaged ("typical") local density of
states is employed to compute the ground state phase diagram of the
Anderson-Hubbard model at half-filling. This non-perturbative approach is
sensitive to Anderson localization on the one-particle level and hence can
detect correlated metallic, Mott insulating and Anderson insulating phases and
can also describe the competition between Anderson localization and
antiferromagnetism. Second, we investigate the effect of binary alloy disorder
on ferromagnetism in materials with -electrons described by the periodic
Anderson model. A drastic enhancement of the Curie temperature caused by
an increase of the local -moments in the presence of disordered conduction
electrons is discovered and explained.Comment: 17 pages, 7 figures, final version, typos corrected, references
updated, submitted to Eur. Phys. J. for publication in the Special Topics
volume "Cooperative Phenomena in Solids: Metal-Insulator Transitions and
Ordering of Microscopic Degrees of Freedom
The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results
After a brief discussion of the Bogoliubov inequality and possible
generalizations thereof, we present a complete review of results concerning the
Mermin-Wagner theorem for various many-body systems, geometries and order
parameters. We extend the method to cover magnetic phase transitions in the
periodic Anderson Model as well as certain superconducting pairing mechanisms
for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations
in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of
Physics: Condensed Matte
Magnetic Correlations in the Two Dimensional Anderson-Hubbard Model
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.Comment: 10 pages, REVTeX, 14 figures included using psfig.st
Disorder-enhanced delocalization and local-moment quenching in a disordered antiferromagnet
The interplay of disorder and spin-fluctuation effects in a disordered
antiferromagnet is studied. In the weak-disorder regime (W \le U), while the
energy gap decreases rapidly with disorder, the sublattice magnetization,
including quantum corrections, is found to remain essentially unchanged in the
strong correlation limit. Magnon energies and Neel temperature are enhanced by
disorder in this limit. A single paradigm of disorder-enhanced delocalization
qualitatively accounts for all these weak disorder effects. Vertex corrections
and magnon damping, which appear only at order (W/U)^4, are also studied. With
increasing disorder a crossover is found at W \sim U, characterized by a rapid
decrease in sublattice magnetization due to quenching of local moments, and
formation of spin vacancies. The latter suggests a spin-dilution behavior,
which is indeed observed in softened magnon modes, lowering of Neel
temperature, and enhanced transverse spin fluctuations.Comment: 12 pages, includes 8 postscript figures. To appear in Physical Review
B. References adde
Constrained-path quantum Monte Carlo simulations of the zero-temperature disordered two-dimensional Hubbard model
We study the effects of disorder on long-range antiferromagnetic correlations
in the half-filled, two dimensional, repulsive Hubbard model at 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 < 2t in the case of bond disorder, and U <
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, we find a critical bond disorder of Vc = (1.6 +- 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 Vc =
(5.0 +- 0.5)t at U=4t.Comment: Revtex, 13 pages, 15 figures. Minor changes to title and abstract,
discussion and references added, figures 5, 6, 8, 9 replaced with easier to
read version
Two-Particle-Self-Consistent Approach for the Hubbard Model
Even at weak to intermediate coupling, the Hubbard model poses a formidable
challenge. In two dimensions in particular, standard methods such as the Random
Phase Approximation are no longer valid since they predict a finite temperature
antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The
Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as
particle conservation, the Pauli principle, the local moment and local charge
sum rules. The self-energy formula does not assume a Migdal theorem. There is
consistency between one- and two-particle quantities. Internal accuracy checks
allow one to test the limits of validity of TPSC. Here I present a pedagogical
review of TPSC along with a short summary of existing results and two case
studies: a) the opening of a pseudogap in two dimensions when the correlation
length is larger than the thermal de Broglie wavelength, and b) the conditions
for the appearance of d-wave superconductivity in the two-dimensional Hubbard
model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems",
Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages.
Misprint in Eq.(23) corrected (thanks D. Bergeron
Single-particle excitations under coexisting electron correlation and disorder: a numerical study of the Anderson-Hubbard model
Interplay of electron correlation and randomness is studied by using the
Anderson-Hubbard model within the Hartree-Fock approximation. Under the
coexistence of short-range interaction and diagonal disorder, we obtain the
ground-state phase diagram in three dimensions, which includes an
antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic
insulator (Anderson-localized insulator) and a paramagnetic metal. Although
only the short-range interaction is present in this model, we find
unconventional soft gaps in the insulating phases irrespective of electron
filling, spatial dimensions and long-range order, where the single-particle
density of states (DOS) vanishes with a power-law scaling in one dimension (1D)
or even faster in two dimensions (2D) and three dimensions (3D) toward the
Fermi energy. We call it soft Hubbard gap. Moreover, exact-diagonalization
results in 1D support the formation of the soft Hubbard gap beyond the
mean-field level. The formation of the soft Hubbard gap cannot be attributed to
a conventional theory by Efros and Shklovskii (ES) owing the emergence of soft
gaps to the long-range Coulomb interaction. Indeed, based on a picture of
multivalley energy landscape, we propose a phenomenological scaling theory,
which predicts a scaling of the DOS in perfect agreement with the numerical
results. We further discuss a correction of the scaling of the DOS by the
long-range part of the Coulomb interaction, which modifies the scaling of Efros
and Shklovskii. Furthermore, explicit formulae for the temperature dependence
of the DC resistivity via variable-range hopping under the influence of the
soft gaps are derived. Finally, we compare the present theory with experimental
results of SrRu_{1-x}Ti_xO_3.Comment: 22 pages, 19 figure