Related papers: Summing graphs for random band matrices
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous…
We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be…
Optically active networks show feature-rich emission that depends on the fine details of their geometry, and find diverse applications in random lasers, sensing devices and photonics processors. In these and other systems, a thorough and…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through…
In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle…
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive a new formula for the Stieljes transform of the spectral…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
Several density-matrix renormalization group methods have been proposed to compute the momentum- and frequency-resolved dynamical correlation functions of low-dimensional strongly correlated systems. The most relevant approaches are…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively.…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices we call graph matrices. While the classical case of symmetric matrices with independent random entries (Wigner's matrices) is a special case, in…
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…