相关论文: Eigenfunction entropy and spectral compressibility…

We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)-dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the…

We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…

In this work we calculate the Cram\'{e}r-Rao, the Fisher-Shannon and the L\'{o}pez-Ruiz-Mancini-Calbert (LMC) complexity measures for eigenstates of a deformed Schr\"{o}dinger equation, being this intrinsically linked with…

We investigate the critical behaviour of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model.Series expansions are calculated for the linear chain…

For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that…

We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\times n$ matrices with i.i.d. complex Gaussian entries with a few…

The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like…

In this paper we study the notion of critical dimension of random simplicial complexes in the general multi-parameter model described in our previous papers of this series. This model includes as special cases the Linial-Meshulam-Wallach…

We develop techniques to compute the k-th Moment of the Eigenvalue-statistic for a random Matrix M the entries of which do not have to be necessarily Independent. The dependence is controlled via an equivalence relation on the pairs of the…

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with…

The dynamical scaling for statistics of critical multifractal eigenstates proposed by Chalker is analytically verified for the critical random matrix ensemble in the limit of strong multifractality controlled by the small parameter $b\ll…

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…

The eigenstate entanglement entropy has been recently shown to be a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, a unique feature of the average eigenstate entanglement entropy (over all…

A formidable perspective in understanding quantum criticality of a given many-body system is through its entanglement contents. Until now, most progress are only limited to the disorder-free case. Here, we develop an efficient scheme to…

We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…

Using the analytical expressions for the genuine eigenfunctions $\varphi_{\mu\nu}(z)$ and eigenvalues $E_{\mu,\nu}$, of open, bounded and quasi-bounded finite periodic systems, we derive the eigenfunctions space-inversion symmetry…

We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's…

We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle eigenfunctions of the entanglement…