The 𝛽 ensemble is a prototypical model of a single-particle system on a one-dimensional disordered lattice with inhomogeneous nearest-neighbor hopping. The corresponding nonergodic phase has an anomalous critical energy scale, 𝐸𝑐: Correlations are present above and absent below 𝐸𝑐, as reflected in the number variance. We study the dynamical properties of the 𝛽 ensemble where the critical energy controls the characteristic timescales. In particular, the spectral form factor equilibrates at a relaxation time 𝑡R≡𝐸−1𝑐, which is parametrically smaller than the Heisenberg time, 𝑡H, given by the inverse of the mean level spacing. Incidentally, the dimensionless relaxation time, 𝜏R≡𝑡R/𝑡H≪1 is equal to the Dyson index, 𝛽. We show that the energy correlations are absent within a temporal window 𝑡R<𝑡<𝑡H, which we term as the correlation void. This is in contrast to the mechanism of equilibration in a typical many-body system. We analytically explain the qualitative behavior of the number variance and the spectral form factor of the 𝛽 ensemble by a spatially local mapping to the Anderson model.

Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality, which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates that allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1D tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions, which are in agreement with numerical simulations.

Models with correlated disorder are rather common in physics. In some of them, like the Aubry-André (AA) model, the localization phase diagram can be found from the (self)duality with respect to the Fourier transform. In others, like the all-to-all translation-invariant Rosenzweig-Porter (TI RP) ensemble or the many-body localization (MBL), one needs to develop more sophisticated and usually phenomenological methods to obtain the localization transition. In addition, such models contain not only localization, but also the ergodicity-breaking transition in the Hilbert-space eigenstate structure, giving way to the nonergodic (i.e., MBL) phase of states with nontrivial fractal dimensions Dq>0. In this work, we suggest a method to calculate both the above transitions and a lower bound to the fractal dimensions D2 and D∞, relevant for the physical observables. To verify this method, we apply it to the class of long-range (self-)dual models, interpolating between a tight-binding ballistic model and TI RP via both power-law dependencies of the hopping terms and the on-site disorder correlations, and, thus, being out of the validity range of the previously developed methods. We show that the interplay of the correlated disorder and the power-law decaying hopping terms leads to the emergence of the two types of nonergodic phases in the entire range of parameters, even without having any quasiperiodicity of the AA potential. The analytical results of the above method are in full agreement with the extensive numerical calculations.

We report on the induction of magnetization in Rydberg systems by means of the inverse Faraday effect and propose the appearance of the effect in two such systems: Rydberg atoms proper and shallow dopants in semiconductors. Rydberg atoms are characterized by a large orbital radius. This large radius gives such excited states a large angular moment, which when driven with circularly polarized light translates to a large effective magnetic field Beff. We calculate this effect to generate effective magnetic fields of O(1μT)×(ω1THz)-1(I10Wcm-2)n4 in the Rydberg states of atoms such as Rb and Cs for off-resonant photon beams with frequency ω and intensity I expressed in units of the denominators and n the principal quantum number. Additionally, terahertz spectroscopy of phosphorus-doped silicon reveals a large cross section for excitation of shallow dopants to Rydberg-like states, which even for small n have the potential to be driven similarly with circularly polarized light to produce an even larger magnetization. Our theoretical calculations estimate Beff as O(102T) for Si:P with a beam intensity of 108Wcm-2.

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.

Typically, metallic systems localized under strong disorder exhibit a transition to delocalization as the kinetic terms increase. In this Letter, we reveal the opposite effect—increasing kinetic terms leads to an unexpected reduction of mobility, enhancing localization of the system, and even leading to reentrant delocalization transitions. Specifically, we add a nearest-neighbor hopping with amplitude 𝜅 to the Rosenzweig-Porter (RP) model with fractal on-site disorder and surprisingly see that, as 𝜅 grows, the system initially tends to localization from the fractal phase, but then reenters the ergodic phase. We build an analytical framework to explain this re-entrant behavior, supported by exact diagonalization results. The interplay between the spatially local 𝜅 term, insensitive to fractal disorder, and the energy-local RP coupling, sensitive to fine-level spacing structures, drives the observed reentrant behavior. This mechanism offers a distinct pathway to reentrant localization phenomena in many-body quantum systems.

Motivated by a series of recent works, an interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase and are of high demand in quantum annealing and machine learning. Inspired by the success of the Rosenzweig-Porter (RP) model with Gaussian-distributed hopping elements, several RP -like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of frac-tal dimensions for a generic RP model and investigate what features of the RP Hamil-tonians can be responsible for the multifractal phase emergence. We conclude that the only feature contributing to a genuine multifractality is the on-site energies' distribution, meaning that no random matrix model with a statistically homogeneous distribution of diagonal disorder and uncorrelated off-diagonal terms can host a multifractal phase.

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.

Focusing on Bethe-Ansatz integrable models, robust to both time-reversal symmetry breaking and disorder, we consider the Russian Doll Model (RDM) for finite system sizes and energy levels. Suggested as a time-reversal-symmetry breaking deformation of Richardson’s model, the well-known and simplest model of superconductivity, RDM revealed an unusual cyclic renormalization group (RG) over the system size N, where the energy levels repeat themselves, shifted by one after a finite period in ln N, supplemented by a hierarchy of superconducting condensates, with the superconducting gaps following the so-called Efimov (exponential) scaling. The equidistant single-particle spectrum of RDM made the above Efimov scaling and cyclic RG to be asymptotically exact in the wideband limit of the diagonal potential. Here, we generalize this observation in various respects. We find that, beyond the wideband limit, when the entire spectrum is considered, the periodicity of the spectrum is not constant, but appears to be energy-dependent. Moreover, we resolve the apparent paradox of shift in the spectrum by a single level after the RG period, despite the disappearance of a finite fraction of energy levels. We also analyze the effects of disorder in the diagonal potential on the above periodicity and show that it survives only for high energies beyond the energy interval of the disorder amplitude. Our analytic analysis is supported with exact diagonalization.

In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction 𝛽 of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in a certain range of parameters (d,𝛽) at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.