Related papers: Supersymmetry and Localization in the Quantum Hall…
We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism…
The well-established non-Bloch band theory predicts exponential localization of skin-mode eigenstates in one-dimensional (1D) non-Hermitian systems. Recent studies, however, have uncovered anomalous algebraic localization in higher…
We analyze the quantum phase transition between a semimetal and a superfluid in a model of attractively interacting fermions with a linear dispersion. The quantum critical properties of this model cannot be treated by the Hertz-Millis…
We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest Landau level. Employing a supersymmetric technique,…
We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudo-site density matrix renormalization group (DMRG) technique. Performing a careful finite-size…
We obtain the field-theory representations of several network models that are relevant to 2D transport in high magnetic fields. Among them, the simplest one, which is relevant to the plateau transition in the quantum Hall effect, is…
A review is given of quantum network models in class C which, on a suitable 2d lattice, describe the spin quantum Hall plateau transition. On a general class of graphs, however, many observables of such models can be mapped to those of a…
We study the quantum dynamics of conversion of composite bosons into fermionic fragment species with increasing densities of bound fermion pairs using the open quantum system approach. The Hilbert space of $N$-state-function is decomposed…
We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them…
A model consisting of a mixture of superconducting and quantum links is proposed to describe the integer quantum Hall transition. The quantum links correspond to tunneling of electrons between trajectories trapped in adjacent potential…
We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical…
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical…
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a modular symmetry group commuting with the renormalization group flow and hence mapping different phases of…
The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. We discuss possible experimental measurements of the half-integer Hall conductance $g_{xy}$ of topological insulator surface states…
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum…
This paper introduces a novel method to account for quantum disorder effects into the classical drift-diffusion model of semiconductor transport through the localization landscape theory. Quantum confinement and quantum tunneling in the…
Quantum transport through disordered structures is inhibited by (Anderson) localization effects. The disorder can be either topological as in random networks or energetical as in the original Anderson model. In both cases the eigenstates of…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…