This work demonstrates that sparse long-range random bonds on a one-dimensional lattice alone can generate quantum-chaotic spectral correlations and also drive a localization transition in a noninteracting single-particle Hamiltonian. The model is a one-dimensional ring in which each pair of sites is connected independently with a probability $p_{ij}= d_{ij}^{-(1+\sigma)}$. Each bond carries identical unit hopping and on-site disorder is absent. Despite the absence of on-site disorder and interaction, the model displays quantum chaotic spectra with Gaussian orthogonal ensemble (GOE) level statistics at small $\sigma$ and localized eigenstates with Poisson statistics at larger $\sigma$. The transition occurs in the range $ 0.80 \lesssim \sigma_c \lesssim 0.85$, far above the summability threshold of the mean hopping profile ($\sigma=0$). A Gaussian field theory retaining only the mean and variance of the Bernoulli bonds instead predicts a threshold at $\sigma=1$, suggesting that higher cumulants are infrared-relevant. Our findings hint towards a universality class that is distinct from both the power-law random banded matrix model and the standard Anderson transition.
We study local eigenvalue statistics and dynamical (de)-localization properties for long-range Anderson models, including the fractional Anderson model. These systems are random Anderson-type perturbations of operators with long-range (non random) hopping terms of the form $|T(n,m)| \sim \|n-m\|^{-(d+2\beta)}$ for $\be...
P. Hislop, Rodrigo Matos, C. Rojas-Molina· 0 citations
In a slowly varying aperiodic potential $h_i=h\cos(2\pi\beta i^n+\phi)$ with random power-law density interactions $V_{ij}/|i-j|^\alpha$, the resonant-object ensemble changes across $\alpha=2n$, wherever Hartree fragmentation is operative, from isolated two-level bonds to a mixture of fragmented multi-site clusters and...
A self-contained statistical-mechanics treatment of a single quantum harmonic oscillator is presented, whose frequency $\omega$ is drawn from a folded Gaussian distribution: $\omega=|\xi|$ with $\xi\sim\mathcal{N}(\mu,\sigma^2)$. The exact integral representations for the partition function, internal energy, free energ...
We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\to\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-r...
M. Bahovadinov, Faridun N. Jalolov, V. E. Kravtsov et al.· 1 citation
We study the thermalization in the random free fermion model by a detailed random-matrix analysis. By computing the ensemble average and fluctuations of $\operatorname{Tr}(A\rho(t))$ for a single-particle observable $A$, we derive the thermalization function $g^2(t/\tau_\lambda)$ with $\tau_\lambda = \hbar/(2\eta\sqrt{...
Nearest-neighbor (NN) tight-binding models (TBMs) on plaquette-centered $\{ 10,3\}$ (Schl\"afli symbol), $\{ 8,3\}$, and $\{ 8,4\}$ hyperbolic lattices on a Poincar\'e disk with open boundary conditions display a vanishing, a finite, and a diverging density of states (DOS) near zero energy (band center), respectively,...
Sheersh Sen, Christopher A. Leong, Bitan Roy· 0 citations
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