Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLevel statistics for quantum $k$-core percolation
96
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Quantum $k$-core percolation is the study of quantum transport on $k$-core percolation clusters where each occupied bond must have at least $k$ occupied neighboring bonds. As the bond occupation probability, $p$, is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the lengthscale for the disorder, $l_d$, is much greater than the coherence length, $l_c$, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrate that for $k=3$ the metal-insulator transition (MIT) is discontinuous, suggesting a new universality class of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability $p$ and system size on a Bethe-like lattice. The level spacing analysis suggests that for $k=0$, $p_q$, the quantum percolation critical probability, is greater than $p_c$, the geometrical percolation critical probability, and the transition is continuous. In contrast, for $k=3$, $p_q=p_c$ and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new universality class of disorder-driven quantum MITs.
rate research
Read More
Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for $k=3$ that the random first-order phase transition in the geometry also drives the onset of quantum conduction giving rise to a new universality class of Anderson localization transitions.
The local distribution of exciton levels in disordered cyanine-dye-based molecular nano-aggregates has been elucidated using fluorescence line narrowing spectroscopy. The observation of a Wigner-Dyson-type level spacing distribution provides direct evidence of the existence of level repulsion of strongly overlapping states in the molecular wires, which is important for the understanding of the level statistics, and therefore the `functional properties, of a large variety of nano-confined systems.
We numerically study the level statistics of the Gaussian $beta$ ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices $beta = 1,2,4$ to the continuous range $0 < beta < infty$. The Gaussian $beta$ ensemble covers Poissonian level statistics for $beta to 0$, and provides a smooth interpolation between Poissonian and Wigner-Dyson level statistics. We establish the physical relevance of the level statistics of the Gaussian $beta$ ensemble by showing near-perfect agreement with the level statistics of a paradigmatic model in studies on many-body localization over the entire crossover range from the thermal to the many-body localized phase. In addition, we show similar agreement for a related Hamiltonian with broken time-reversal symmetry.
The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation can be too restrictive by indicating that the self-correlation imposes a constraint on the spectral form factor integrated over time. More generally, we indicate that each expansion coefficient of the two-point correlation function imposes a constraint on the properly weighted time-integrated spectral form factor. We discuss how these constraints can affect the interpretation of the spectral form factor as a probe for ergodicity. We propose a new probe, which eliminates the effect of the constraint imposed by the self-correlation. The use of this probe is demonstrated for a model of randomly incomplete spectra and a Floquet model supporting many-body localization.
We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
