We investigate the Anderson transition found in the spectrum of the Dirac operator of Quantum Chromodynamics (QCD) at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determi
ne the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high-temperature, and further support that it belongs to the 3D unitary Anderson model class.
The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been performed on syste
ms with linear sizes up to $L=140$. The multifractal dimensions, exponents $D_q$ and $alpha_q$, have been determined in the range of $0leq qleq 1$. Our results confirm that this problem belongs to the same universality class as the three dimensional Anderson model, the critical exponent of the localization length was found to be $ u=1.622pm 0.035$. The mulifractal function, $f(alpha)$, appears to be universal, however, the exponents $D_q$ and $alpha_q$ produced anomalous variations along the phase boundary, $p_c^Q(E)$.
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization. The two-s
ite approximation is solved analytically and shown to capture the essential features found in numerical simulations on one-, two- and three-dimensional systems. Further improvement has been obtained by solving a three-site model.
In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate
that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.
Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum compu
tation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.
