Related papers: Critical spectral statistics in two-dimensional in…
We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-Andr\'{e} model. By analyzing the Lyapunov exponent and localization length, we…
We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the…
We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
In this work, we explore an unconventional class of problems in the study of (quantum) critical phenomena, termed ''deep boundary criticality''. Traditionally, critical systems are analyzed with two types of perturbations: those uniformly…
Using the density matrix renormalization group algorithm, we study the model of spinless fermions with nearest-neighbor interaction on a ring in the presence of disorder. We determine the spatial decay of the density induced by a defect…
Based on the mathematical model of a statistical system with scalar interaction of fermions formulated earlier, a cosmological model based on a two-component statistical system of scalar charged degenerate fermions interacting with an…
We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field…
Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two dimensional random potential. When we increase the system size $L$ at fixed particle density, the size dependence of the average inverse…
We study a two-dimensional system of two Coulombically interacting electrons in an external harmonic confining potential. More precisely, we present calculations for the singlet ground-state of the system. We explain the nature of the…
We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at $T\sim 0$. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using…
We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched…
We present a new numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
We study the consequences of long-range Coulomb interactions at the critical points between integer/fractional quantum Hall states and an insulator. We use low energy theories for such transitions in anyon gases in the presence of an…
We use a Hartree-Fock-Koopmans approach to study spin and interaction effects in a diffusive or chaotic quantum dot. In particular, we derive the statistics of the spacings between successive Coulomb-blockade peaks. We include fluctuations…
We study level correlations in a two-dimensional system with a long-range random potential and strong spin-orbit (SO) splitting of the spectrum. The level correlations for sufficiently large splitting are shown to be described by orthogonal…
Possibility of electronic charge and spin separation leading to charge density wave and spin density wave is well established in one dimensional systems in presence and absence of Coulomb interaction. We start from quasi one dimension and…
We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 space-time dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators…
We study the problem of two interacting particles in the classical Harper model in the regime when one-particle motion is absolutely bounded inside one cell of periodic potential. The interaction between particles breaks integrability of…