Ferromagnetism in the Hubbard Model on fcc-type lattices

The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges.Comment: typos corrected, references updated, discussion extente

Correlated-Electron Theory of Strongly Anisotropic Metamagnets

We present the first correlated-electron theory of metamagnetism in strongly anisotropic antiferromagnets. Quantum-Monte-Carlo techniques are used to calculate the field vs. temperature phase diagram of the infinite-dimensional Hubbard model with easy axis. A metamagnetic transition scenario with 1.~order and 2.~order phase transitions is found. The apparent similarities to the phase diagram of FeBr$_2$ and to mean-field results for the Ising model with competing interactions are discussed.Comment: 4 pages, RevTeX + one uuencoded ps-file including 3 figure

Molecular mechanisms underlying cortical (mal)formation: case studies of ESCO2 and EXOSC10

This work focuses on elucidating the molecular mechanisms that control the cortical development. Identification of genes and factors that direct the development of the cerebral cortex will both tell us about their disease-related importance and improve our understanding of the normal formation and malformation of the cortex. In the first part, we performed transcriptome analysis to determine the molecular profile of IPCs, which play a crucial role in cortical formation as they generate the majority of cortical neurons. Accordingly, we sorted TBR2+ IPCs from the embryonic mouse cortex and analysed gene expression profiles of TBR2+ IPCs versus TBR2- cell populations. We identified different levels of key genetic factors regulating chromatid segregation, cell-cycle progression, transcription, and cell signaling. Remarkably, in humans, mutations of several identified IPC genes are linked to various cortical malformations, like microcephaly and macrocephaly, corpus callosum defects, and neurological deficits. For example, mutations in the cohesin acetyltransferase ESCO2, one of the newly identified IPC genes, cause severe malformations including microcephaly. We showed that deficiency of ESCO2 in the developing mouse cortex leads to severe loss of IPCs, resulting in cortical malformation. We thereby demonstrate the identification of a central genetic factor of IPC genesis. Our molecular profiling data reveal novel molecular characteristics of IPCs and offer a resource for future investigations. Recent sequencing analyses of cortical malformations revealed a multifarious genetic landscape. In our pilot work, we identified novel microcephaly-related mutations in a gene encoding EXOSC10, a core subunit of the RNA-decay exosome complex. In the second part of this work, we characterized the cortical phenotypes of EXOSC10cKO mutants. We showed that EXOSC10 is essential for forebrain formation. EXOSC10 deficiency in the developing mouse cortex causes massive apoptosis in cortical cells resulting in cortical malformation. We found that EXOSC10 binds and degrades mRNA coding for P53 signaling-mediators, like AEN and BBC3. Additionally, our studies indicate that EXOSC10 plays a role in regulating the differentiation of cortical progenitors. It might do so via degrading transcripts of the SHH/WNT-β catenin signaling pathways. Further investigations are needed to illuminate this additional role of EXOSC10. In conclusion, our study reveals an essential role of EXOSC10 in suppressing the P53, SHH/WNT-β catenin pathways, which are indispensable for cell survival, neurogenesis and normal cortical formation. Our findings of the mouse model correspond to observations of humans with microcephaly linked to EXOSC10 mutations.2021-09-2

Inhomogeneous metallic phase upon disordering a two dimensional Mott insulator

We find that isoelectronic disorder destroys the spectral gap in a Mott-Hubbard insulator in 2D leading, most unexpectedly, to a new metallic phase. This phase is spatially inhomogeneous with metallic behavior coexisting with antiferromagnetic long range order. Even though the Mott gap in the pure system is much larger than antiferromagnetic exchange, the spectral gap is destroyed locally in regions where the disorder potential is high enough to overcome the inter-electron repulsion thereby generating puddles where charge fluctuations are enhanced. With increasing disorder, these puddles expand and concomitantly the states at the Fermi energy get extended leading to a metallic phase. We discuss the implications of our results for experiments.Comment: (4 pages, 5 figures

Ordered states in the disordered Hubbard model

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 into 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.Comment: 17 pages, including 8 figures. Paper for Festschrift in honor of Hans van Leeuwen's 65th birthda

Non-perturbative approaches to magnetism in strongly correlated electron systems

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough $U$. Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of $U$ above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view.Comment: 11 pages, Latex, and 6 postscript figures; Z. Phys. B, in pres

Disorder- and correlation-driven metal-insulator transitions

Metal-insulator transitions driven by disorder (Delta) and/or by electron correlations (U) are investigated within the Anderson-Hubbard model with local binary-alloy disorder using a simple but consistent mean-field approach. The Delta-U phase diagram is derived and discussed for T=0 and finite temperatures.Comment: 2 pages, 2 figures, submitted to the SCES'04, Ref.4 update

Two-particle propagator and magnetic susceptibility in the Hubbard model- An improved treatment

We treat the two-particle Green's function in the Hubbard model using the recently developed tau-CPA, a hybrid treatment that applies the coherent-potential approximation (CPA) up to a time tau related to the inverse of the band width, after which the system is averaged using the virtual-crystal approximation (VCA). This model, with suitable approximations, does predict magnetism for a modified Stoner criterion. The evaluation of the two-particle propagator in the tau-CPA requires the solution of the pure CPA, within whose formalism the vertex correction and the weighted Green's functions are obtained. The dynamical susceptibility, including the vertex correction and the weighted scattering by the residual interaction, is calculated and shows a spin wave spectrum in the ferromagnetic regime