Related papers: Localization, Coulomb interaction, topological pri…
We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkelstein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as…
This work discusses the effect of topology in the frame of direct Coulomb interactions, considering two distinct geometries, namely the Hall bar and the Corbino disc. In the mainstream approaches to the quantized Hall effect, the…
Within the Grassmannian $U(2N) / U(N) \times U(N)$ non-linear $\sigma $ model representation of localization one can study the low energy dynamics of both the free and interacting electron gas. We study the cross-over between these two…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
Recent work on the temperature-driven delocalization in the quantum Hall regime is reviewed, with emphasis on the role of electron-electron interactions and the correlation properties of disorder. We have stressed (i) the crucial role of…
We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime…
The impact of Coulomb interaction on the electronic properties of a quantum spin-Hall insulator is studied using quantum cluster methods, disentangling local from non-local effects. We identify different regimes, according to the value of…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We report on numerical studies of the influence of Coulomb interactions on localization of electronic wavefunctions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied…
We study variable range hopping in the quantum Hall effect regime in the presence of a metallic gate parallel to the plane of a two-dimensional electron gas. Screening of the Coulomb interaction by the gate causes the partial ``filling'' of…
We discuss the role of direct Coulomb interaction on the bulk insulator of the integer quantized Hall effect that bridges the topological insulators and the conductance quantization. We investigate the magneto-transport properties of a…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb…
We study the quantum Hall effect in a two-dimensional homogeneous electron gas coupled to a quantum cavity field. As initially pointed out by Kohn, Galilean invariance for a homogeneous quantum Hall system implies that the electronic center…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
We numerically investigate how electron-electron interactions influence the transport properties of disordered electrons in two dimensions. Our study is based on the quantum Coulomb glass model appropriately generalized to include the spin…
We use the non-equilibrium bosonization technique to investigate effects of the Coulomb interaction on quantum Hall edge states at filing factor nu=2, partitioned by a quantum point contact (QPC). We find, that due to the integrability of…
The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it…
It was shown that tunneling current flowing through a system with Coulomb correlations leads to charge redistribution between the different localized states. Simple model consisting of two electron levels have been analyzed by means of…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…