Related papers: Two-eigenfunction correlation in a multifractal me…
We report a new attractive critical point occurring in the Anderson localization scaling flow of symplectic models on fractals. The scaling theory of Anderson localization predicts that in disordered symplectic two-dimensional systems weak…
The spatial extension and complexity of the eigenfunctions of an open finite-size two-dimensional (2D) random system are systematically studied for a random collection of systems ranging from weakly scattering to localized. The…
Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the…
An ab initio approach formulated under an entropy-inspired repartitioning of the electronic Hamiltonian is presented. This ansatz produces orbital eigenvalues each shifted by entropic contributions expressed as subsets of scaled pair…
A particle initially in a pure state but interacting with some environment evolves into a discrete ensemble of pure states, the eigenstates of its reduced density operator, with ensemble probabilities given by the corresponding eigenvalues.…
We derive an exact result for the averaged Feynman propagator and the corresponding density of states of an electron in two dimensions in a perpendicular homogeneous magnetic field and a Gaussian random potential with long-range spatial…
The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…
Recent experiments have employed rapidly expanding toroidal Bose-Einstein condensates (BECs) to mimic the inflationary expansion in the early universe. One expected signature of the expansion in such experiments is spontaneous particle…
In the electron-phonon model, the influence of nonmagnetic impurities on the transition temperature of superconductors is revisited. Anderson's pairing condition between time-reversed eigenstate pairs is derived from the physical constraint…
The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle…
We study the entanglement spectrum of highly excited eigenstates of two known models that exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
We analyze the ergodic properties of a metallic wavefunction for the Anderson model in a disordered random-regular graph with branching number $k=2.$ A few q-moments $I_q$ associated with the zero energy eigenvector are numerically computed…
Recent high resolution Compton scattering experiments clearly reveal that there are fundamental limitations to the conventional local density approximation (LDA) based description of the ground state electron momentum density (EMD) in…
The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed…
Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum and anomalous quantum Hall insulator, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have…
A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently…
Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this…
This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all…
We study ground state and finite temperature properties of disordered heavy fermion metals by using a generalization of dynamical mean field theory which incorporates Anderson localization effects. The emergence of a non-Fermi liquid…