Magnetism, electronic transport, and disorder in strongly correlated systems

Abstract

This thesis investigates the magnetic, spectral, and transport properties of strongly correlated electronic systems, with a primary focus on the Hubbard model and its extensions relevant for real materials. Within the dynamical mean-field theory (DMFT) framework, different regimes of interaction strength, temperature, doping, and magnetic field are explored, highlighting the central role of local electronic correlations in shaping spectral reconstruction and nontrivial transport responses. For the antiferromagnetic Hubbard model under a Zeeman field, magnetoresistance and local metamagnetism are characterized, revealing the coexistence of distinct energy scales associated with charge and spin degrees of freedom. A minimal, purely correlation-driven mechanism for generating spin-polarized charge transport in structurally conventional collinear antiferromagnets is identified, controlled by the simultaneous breaking of particle--hole symmetry and antiferromagnetic sublattice equivalence. Finally, these concepts are applied to correlated materials with strong spin--orbit coupling, such as Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$, and to nanoparticle solids dominated by Coulomb blockade and disorder. The results show how ideas developed in correlated lattice models provide a unified interpretation of metal--insulator transitions and spectral reconstruction in complex systems.

Figures (43)

• Figure 1: Schematic illustration of the Hubbard modelvollhardt2018. Electrons, which carry spin ($\uparrow$ or $\downarrow$), move from one lattice site to another with hopping amplitude $t$. Quantum dynamics gives rise to fluctuations in the site occupations, as indicated in the lower sequence: a lattice site may be empty, singly occupied ($\uparrow$ or $\downarrow$), or doubly occupied. When two electrons occupy the same lattice site, they interact with energy $U$.
• Figure 2: Phase diagram of V$_{2}$O$_{3}$ as a function of pressure (or Cr/Ti substitution) and temperature. The illustrations schematically represent the nature of each phase (paramagnetic Mott insulator, paramagnetic metal, and antiferromagnetic Mott insulator) Georges2007.
• Figure 3: Schematic finite-temperature phase diagram of the doped Hubbard model, according to the experimental and numerical results presented in Mazurenko et al.Mazurenko2017. The figure illustrates the main phases that emerge upon moving away from half filling in the intermediate-coupling regime $(U/t\sim6-8)$. The red arrows indicate experimental trajectories explored using cold atoms in optical lattices.
• Figure 4: Spectral density $A(\omega)$ of the Anderson impurity model in three characteristic regimes: $U=0$ (blue line), moderate $U>0$ (orange line), and $U\gg\Gamma$ (red line), corresponding to the Kondo regime.
• Figure 5: Self-consistent solution of the DMFT equations.