Nonergodic extended states in the β ensemble

Probing multi-mobility edges in quasiperiodic mosaic lattices

The mobility edge (ME) is a crucial concept in understanding localization physics, marking the critical transition between extended and localized states in the energy spectrum. Anderson localization scaling theory predicts the absence of ME in lower dimensional systems. Hence, the search for exact MEs, particularly for single particles in lower dimensions, has recently garnered significant interest in both theoretical and experimental studies, resulting in notable progress. However, several open questions remain, including the possibility of a single system exhibiting multiple MEs and the continual existence of extended states, even within the strong disorder domain. Here, we provide experimental evidence to address these questions by utilizing a quasiperiodic mosaic lattice with meticulously designed nanophotonic circuits. Our observations demonstrate the coexistence of both extended and localized states in lattices with broken duality symmetry and varying modulation periods. By single-site injection and scanning the disorder level, we could approximately probe the ME of the modulated lattice. These results corroborate recent theoretical predictions, introduce a new avenue for investigating ME physics, and offer inspiration for further exploration of ME physics in the quantum regime using hybrid integrated photonic devices.

Observation of reentrant metal-insulator transition in a random-dimer disordered SSH lattice

The interrelationship between localization, quantum transport, and disorder has remained a fascinating focus in scientific research. Traditionally, it has been widely accepted in the physics community that in one-dimensional systems, as disorder increases, localization intensifies, triggering a metal-insulator transition. However, a recent theoretical investigation [Phys. Rev. Lett. 126, 106803] has revealed that the interplay between dimerization and disorder leads to a reentrant localization transition, constituting a remarkable theoretical advancement in the field. Here, we present the first experimental observation of reentrant localization using an experimentally friendly model, a photonic SSH lattice with random-dimer disorder, achieved by incrementally adjusting synthetic potentials. In the presence of correlated on-site potentials, certain eigenstates exhibit extended behavior following the localization transition as the disorder continues to increase. We directly probe the wave function in disordered lattices by exciting specific lattice sites and recording the light distribution. This reentrant phenomenon is further verified by observing an anomalous peak in the normalized participation ratio. Our study enriches the understanding of transport in disordered mediums and accentuates the substantial potential of integrated photonics for the simulation of intricate condensed matter physics phenomena.

Exploring universality of the β-Gaussian ensemble in complex networks via intermediate eigenvalue statistics

The eigenvalue statistics are an important tool to capture localization to delocalization transition in physical systems. Recently, a β-Gaussian ensemble is being proposed as a single parameter to describe the intermediate eigenvalue statistics of many physical systems. It is critical to explore the universality of a β-Gaussian ensemble in complex networks. In this work, we study the eigenvalue statistics of various network models, such as small-world, Erdős-Rényi random, and scale-free networks, as well as in comparing the intermediate level statistics of the model networks with that of a β-Gaussian ensemble. It is found that the nearest-neighbor eigenvalue statistics of all the model networks are in excellent agreement with the β-Gaussian ensemble. However, the β-Gaussian ensemble fails to describe the intermediate level statistics of higher order eigenvalue statistics, though there is qualitative agreement till n<4. Additionally, we show that the nearest-neighbor eigenvalue statistics of the β-Gaussian ensemble is in excellent agreement with the intermediate higher order eigenvalue statistics of model networks.

Absence of Mobility Edge in Short-Range Uncorrelated Disordered Model: Coexistence of Localized and Extended States

Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we formulate the main principles and provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge. Unexpectedly, this example appears to be given by a well-studied β ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are nonergodic and allows one to analytically estimate their fractal dimensions.

Transport in deformed centrosymmetric networks

Centrosymmetry often mediates perfect state transfer (PST) in various complex systems ranging from quantum wires to photosynthetic networks. We introduce the deformed centrosymmetric ensemble (DCE) of random matrices H(λ)≡H_{+}+λH_{-}, where H_{+} is centrosymmetric while H_{-} is skew-centrosymmetric. The relative strength of the H_{±} prompts the system size scaling of the control parameter as λ=N^{-γ/2}. We propose two quantities, P and C, quantifying centro and skewcentrosymmetry, respectively, exhibiting second-order phase transitions at γ_{P}≡1 and γ_{C}≡-1. In addition, DCE posses an ergodic transition at γ_{E}≡0. Thus equipped with a precise control of the extent of centrosymmetry in DCE, we study the manifestation of γ on the transport properties of complex networks. We propose that such random networks can be constructed using the eigenvectors of H(λ) and establish that the maximum transfer fidelity F_{T} is equivalent to the degree of centrosymmetry P.