Related papers: Spectral statistics near the quantum percolation t…
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
Recently a multifractal object, $Q_{mf}$, was proposed to study percolation properties in a multifractal support. The area and the number of neighbors of the blocks of $Q_{mf}$ show a non-trivial behavior. The value of the probability of…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
Entanglement properties are routinely used to characterize phases of quantum matter in theoretical computations. For example the spectrum of the reduced density matrix, or so-called "entanglement spectrum", has become a widely used…
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…
Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the…
We study the electronic structure of the binary alloy and (quantum) percolation model. Our study is based on a self-consistent scheme for the distribution of local Green functions. We obtain detailed results for the density of states, from…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We consider (1+1)-dimensional QCD coupled to scalars in the adjoint representation of the gauge group SU($N$). This model results from dimensional reduction of the (2+1)-dimensional pure glue theory. In the large-N limit we study the…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We…
In string percolation model, the study of colliding systems at high energies is based on a continuum percolation theory in two dimensions where the number of strings distributed in the surface of interest is strongly determined by the size…
We study the density of states and the optical conductivity of the classical double-exchange model on a site percolated cluster.
The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), we…
The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit…
Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a…