Related papers: Connection between low energy effective Hamiltonia…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
We study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, PT-symmetric systems and systems with real spectra. The…
We study the statistical fluctuations of Lyapunov exponents in the discrete version of the non-integrable perturbed sine-Gordon equation, the dissipative ac+dc driven Frenkel-Kontorova model. Our analysis shows that the fluctuations of the…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
We analyze several ground state related properties of mesoscopic systems using the random interaction matrix model EGOE(1+2)-$\cs$ (or RIMM) for many fermion systems with spin degree of freedom and the Hamiltonian containing pairing and…
Given a specific interacting quantum Hamiltonian in a general spatial dimension, can one access its entanglement properties, such as, the entanglement entropy corresponding to the ground state wavefunction? Even though progress has been…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature,…
Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been…
We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential,…
In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a…
We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the…
By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single…
Coupling constants for the most relevant terms in the low energy effective Hamiltonian of the XXZ spin chain are derived. Using this result we study the low energy (low temperature, weak magnetic field) thermodynamics, finite size effects…
We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and…
A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical…
Recent investigations on the Hamiltonian of excitons by F. Schweiner et al. [Phys. Rev. Lett. 118, 046401 (2017)] revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The…
We consider systems of weakly interacting fermions on a lattice. The corresponding free fermionic system is assumed to have a ground state separated by a gap from the rest of the spectrum. We prove that, if both the interaction and the free…
We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the…
The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of disordered interacting one-dimensional many-particle system is studied. The average of the first entanglement…