Related papers: Level-spectra Statistics in Planar Fractal Tight-B…
Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \textit{Sierpi\'{n}ski} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed…
We consider self-dual transverse-field Ising spin chains with $m$-spin interaction, where the phase transition is of second and first order, for m <= 3 and m>3, respectively. We present a statistical analysis of the spectra of the…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
Using the adiabatic switching of interactions, we establish a condition for the existence of electronic quasiparticles in a Luttinger liquid. It involves a characteristic interaction strength proportional to the inverse square root of the…
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…
A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics…
Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and…
We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of…
We investigate self-organized criticality in a two-dimensional electron gas (2DEG) by introducing a lattice-based model that incorporates electron-electron interactions through the concept of coherence length. Our numerical simulations…
A good quality scaling of the cluster size distributions is obtained for the Lattice Gas Model using the Fisher's ansatz for the scaling function. This scaling identifies a pseudo-critical line in the phase diagram of the model that spans…
The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude…
The level statistics in the two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The…
We give the details of the analysis for critical properties of spin-gap phases in one-dimensional lattice electron models. In the Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes…
We study the absorbing state phase transition in the contact process on the Weighted Planar Stochastic (WPS) Lattice. The WPS lattice is multifractal. Its dual network has a power-law degree distribution function and is also embedded in a…
Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
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…
Using the Anderson model for disordered systems the fluctuations in electron spectra near the metal--insulator transition were numerically calculated for lattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size scaling of…
The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square…
The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the…
We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the…