Related papers: Level statistics of the one-dimensional ionic Hubb…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at…
The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi-Hubbard model with dimerized hopping amplitude and find…
One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a…
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schr\"odinger (or Gross-Pitaevski) equation. Our formula applies…
We study numerically the evolution of energy-level statistics as an integrability-breaking term is added to the XXZ Hamiltonian. For finite-length chains, physical properties exhibit a cross-over from behavior resulting from the Poisson…
We study the level-statistics of a disordered system undergoing the Anderson type metal-insulator transition. The disordered Hamiltonian is a sparse random matrix in the site representation and the statistics is obtained by taking an…
A repulsive Hubbard model with both spin-asymmetric hopping (${t_\uparrow\neq t_\downarrow}$) and a staggered potential (of strength $\Delta$) is studied in one dimension. The model is a compound of the mass-imbalanced (${t_\uparrow\neq…
We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the…
Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics when chaotic, or 2-dimensional (2d) Poisson statistics when integrable. We investigate the spectral properties of a…
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles…
We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…
We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…
We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
It is an well established fact that statistical properties of energy level spectra are the most efficient tool to characterize nonintegrable quantum systems. The study of statistical properties and spectral fluctuation in the interacting…
We consider the level statistics of two-dimensional harmonic oscillators with incommensurable frequencies, which are known to have picket-fence type spectra. We propose a parametric representation for the level-spacing distribution and…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a…