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

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

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

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 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

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

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

Rigorous Results, Cross-Model Justification, and the Transfer of Empirical Warrant: The Case of Many-Body Models in Physics

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation

Evolution of the early to late Archean mantle from Hf-Nd-Ce isotope systematics in basalts and komatiites from the Pilbara Craton

Inferences on the early evolution of the Earth's mantle can be deduced from long-lived radiogenic isotope Lu-176-Hf-176 and systems such as Sm-147-Nd-143, for which both parent and daughter elements largely remain immobile at low metamorphic grades. However, it remains ambiguous when and to what extent mantle-crust differentiation processes had started in the Archean. For a better understanding of Archean mantle-crust evolution, we determined the initial Lu-176-Hf-176, Sm-147-Nd-143, and, in a new approach, the La-138-Ce-138 isotope compositions of a suite of Archean mafic-ultramafic rock samples from the 3.53-2.83 Ga old Pilbara Craton and 2.78-2.63 Ga old Fortescue Group in NW Australia. These rocks represent one of the best-preserved Archean successions worldwide and contain mafic-ultramafic rocks that were erupted during repeated and long-lived pulses of volcanism throughout much of the Archean. Mantlederived mafic-ultramafic rock samples were collected from six major stratigraphic groups of the Pilbara Craton and the overlying Fortescue Group in order to characterize the parental mantle source regions of the lavas and to reconstruct the temporal evolution of the ambient mantle beneath this piece of cratonic lithosphere. In addition, we analyzed contemporaneous TTG-like igneous suites and interbedded sediments in order to reconstruct the lithospheric evolution of the Pilbara Craton. The Hf-Nd-Ce isotope data imply the onset of mantle-crust differentiation in the Pilbara Craton as early as similar to 4.2 Ga, well prior to any of the preserved stratigraphy. Within error, coupled Ce-Nd-Hf isotope arrays all intersect chondritic values, implying that the Earth is of broadly chondritic composition, also for the La-138-Ce-138 isotope system. Mafic rocks usually yield strongly coupled epsilon Hf-(i), epsilon Nd-(i) and epsilon Ce-(i) values that form a mixing line between an evolving depleted upper mantle composition and the primitive mantle value (epsilon Hf-(i) ca. 0.0 to + 3.2, epsilon Nd-(i) ca. +0.2 to +1.7 and epsilon Ce-(i) ca. +0.3 to -0.1). As all Paleoarchean samples lack co-variations between Nb/Th with epsilon Hf-(i) or epsilon Nd-(i), contamination with an enriched crust is unlikely to explain this mixing trend. The most primitive mantle-like mafic samples show elevated Gd-N/Yb-N ratios (2.2-1.4), implying the involvement of a deep-rooted, near-primitive, upwelling mantle that was progressively mixed into the depleted upper mantle. In contrast to the mafic rocks, most, but not all komatiites are decoupled in their initial Hf-Nd-Ce isotope compositions, by having extremely radiogenic epsilon Hf-(i) values at only moderately high epsilon Nd-(i) and low epsilon Ce-(i) values. This decoupling is best explained by the assimilation of mantle domains that underwent early melt depletion in the garnet stability field and evolved at high Lu-176/Hf-176 ratios but at moderate Sm-147/Nd-143 and La-138/Ce-138 ratios over time. The disappearance of rocks with decoupled Hf-Nd isotope compositions after similar to 3.2 Ga is likely linked to decreasing mantle temperatures that were no longer able to melt such refractory mantle domains. Collectively, our new data for mafic rocks from the Pilbara Craton confirm the presence of long-term depleted mantle domains in the early Archean that are not sampled by the zircon Hf isotope record in the Pilbara Craton. (C) 2020 The Authors. Published by Elsevier B.V