Related papers: The Calculation of Two-Particle Quantities in the …
We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative stability estimate between the $N$-body density matrix and…
The Iterated Perturbation Theory (IPT) equations of the Dynamical Mean Field Theory (DMFT) for the half-filled Hubbard model, are solved on nearly real frequencies at various values of the Hubbard parameters $U$, to investigate the nature…
In this tutorial paper, we formulate a two-dimensional integral-equation based method of moments approach for numerically computing the electromagnetic fields scattered from an azimuthally-rough dielectric cylinder or an axially-rough…
A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a…
We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical…
A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P_0={\pm{\pi}/a, {\pi}/a} for a half-filled…
Self-consistent theory of electron localization in disordered systems is generalized for the case of interacting electrons. We propose and critically compare a number of possible self-consistency schemes which take into account the lowest…
We demonstrate that network models for wave mechanical systems with quenched disorder cover the physics of mesoscopic electrons. The models are constructed as a network of random scattering matrices connecting incoming to outgoing wave…
We introduce a mean-field and perturbative approach, based on clusters, to describe the ground state of fermionic strongly-correlated systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product over…
The position of a field-tuned superconductor-insulator quantum transition occuring in disordered thin films is examined within the mean field approximation. Our calculation shows that the microscopic disorder-induced reduction of the…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite size exact…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
In the absence of magnetic field or spin-orbit coupling the one-parameter scaling theory predicts localization of all states in two-dimensional (2D) disordered systems, for any amount of disorder. However, a 2D metallic phase has been…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
The LDA+DMFT method is a very powerful tool for gaining insight into the physics of strongly correlated materials. It combines traditional ab-initio density-functional techniques with the dynamical mean-field theory. The core aspects of the…
Recent experiments by Ralph and Buhrman on zero-bias anomalies in quenched Cu nanoconstrictions (reviewed in the preceding paper, I), are in accord with the assumption that the interaction between electrons and nearly degenerate two-level…
We study electron localization in disordered quantum systems, focusing on both individual eigenstates and thermal states. We employ complex polarization as a numerical indicator to characterize the system's localization length. Furthermore,…
Materials with correlated electrons often respond very strongly to external or internal influences, leading to instabilities and states of matter with broken symmetry. This behavior can be studied theoretically either by evaluating the…
We study the two-dimensional paramagnetic Anderson-Hubbard model using an extension of dynamical mean-field theory that allows us to treat disorder and strong electronic correlations on equal footing. We investigate the scaling of the…