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Ivan M. Khaymovich

Publications and source records attributed to Ivan M. Khaymovich.

At least 19 recordsLinked to original sources
arXiv2026

Inapplicability of Avila's theory in the diamond chain with quasiperiodic disorder

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.

cond-mat.str-el↗
arXiv2026

Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking

We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.

cond-mat.dis-nn↗
arXiv2026

Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians

We explore interpretations of the power-law banded random matrix (PLBRM) ensemble as Hamiltonians of one-dimensional quantum many-body systems. We introduce and compare a number of labeling schemes for assigning random matrix basis indices to many-body basis vectors. We compare the physical properties of the resulting Hamiltonians, focusing on the half-system eigenstate bipartite entanglement entropy. We show and quantify how the different PLBRM phases (ergodic, weakly ergodic, localized), known from the single-particle interpretation, can be interpreted as entanglement transitions in the quantum many-body interpretation. For the weakly ergodic phase, where spectral edge and bulk eigenstates show distinct behavior, we perform a detailed scaling analysis to provide a quantitative picture of the boundaries between different types of entanglement scaling behaviors. In particular, we identify and characterize an intermediate set of eigenstates whose entanglement entropy have volume law scaling but nonvanishing deviation from the Page value expected for maximally ergodic states.

cond-mat.dis-nn↗
arXiv2025

Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model

Typically, metallic systems localized under strong disorder exhibit a transition to \imk{delocalization} %finite conduction as kinetic terms increase. In this work, we reveal the opposite effect~--~increasing kinetic terms leads to an unexpected \imk{reduction of mobility, }%suppression of conductivity, enhancing localization of the system, and even lead to re-entrant 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 re-enters 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 structure, drives the observed re-entrant behavior. This mechanism offers a novel pathway to re-entrant localization phenomena in many-body quantum systems.

cond-mat.dis-nn↗
arXiv2025

Quadratic Hamiltonian approach to heat transport in fermionic systems

We investigate the problem of quantum heat transport, based on the quadratic fermionic systems with help of the Peschel trick of single-particle correlation functions. The efficient numerical method is applied to the particular case of a single mode heat valve and the results are compared to analytical formulae. Comparing several configurations and parameters we perform the systematic analysis of the method to most efficiently and accurately describe the simple quantum heat valve system.

quant-ph↗
arXiv2025

Anomalous energy correlations and spectral form factor in the nonergodic phase of the $β$-ensemble

The $β$-ensemble is a prototypical model of a single particle system on a one-dimensional disordered lattice with inhomogeneous nearest neighbor hopping. Corresponding nonergodic phase has an anomalous critical energy scale, $E_c$: correlations are present above and absent below $E_c$ 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, $t_\mathrm{R} \equiv E_c^{-1}$, which is parametrically smaller than the Heisenberg time, $t_\mathrm{H}$, given by the inverse of the mean level spacing. Incidentally, the dimensionless relaxation time, $τ_\mathrm{R} \equiv t_\mathrm{R}/t_\mathrm{H} \ll 1$ is equal to the Dyson index, $β$. We show that the energy correlations are absent within a temporal window $t_\mathrm{R} < t < t_\mathrm{H}$, 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.

cond-mat.dis-nn↗
arXiv2025

Large inverse Faraday effect for Rydberg states of free atoms and isolated donors in semiconductors

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 ${B}_{\text{eff}}$. We calculate this effect to generate effective magnetic fields of $O(1\,μ\text{T})\times\left( \fracω{1\,\text{THz}} \right)^{-1} \left( \frac{I}{10\,\text{W cm}^{-2}} \right) n^4$ in the Rydberg states of atoms such as Rb and Cs for off-resonant photon beams with frequency omega 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 ${B}_{\text{eff}}$ as $O(10^2\,\text{T})$ for Si:P with a beam intensity of $10^8\,\text{W cm}^{-2}$.

physics.atom-ph↗
arXiv2025

Emergent multifractality in power-law decaying eigenstates

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 which 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.

cond-mat.dis-nn↗
arXiv2024

Refined cyclic renormalization group in Russian Doll model

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.

cond-mat.dis-nn↗
arXiv2024

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.

cond-mat.dis-nn↗
arXiv2024

Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping

Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) \propto r^{-2}$ is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than $2$. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.

cond-mat.dis-nn↗
arXiv2024

Robust extended states in Anderson model on partially disordered random regular graphs

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.

cond-mat.dis-nn↗
arXiv2023

Anatomy of the eigenstates distribution: a quest for a genuine multifractality

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 RosenzweigPorter (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 fractal dimensions for a generic RP model and investigate what features of the RP Hamiltonians 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.

cond-mat.dis-nn↗
arXiv2023

Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder

Rosenzweig-Porter (RP) model has garnered much attention in the last decade, as it is a simple analytically tractable model showing both ergodic--nonergodic extended and Anderson localization transitions. Thus, it is a good toy model to understand the Hilbert-space structure of many body localization phenomenon. In our study, we present analytical evidence, supported by exact numerical computations, that demonstrates the controllable tuning of the phase diagram in the RP model by employing on-site potentials with a non-trivial fractal dimension instead of the conventional random disorder. We demonstrate that doing so extends the fractal phase and creates unusual dependence of fractal dimensions of the eigenfunctions. Furthermore, we study the fate of level statistics in such a system and analyze the return probability of a wave packet localized at a single site to provide a dynamical test-bed for our theory.

cond-mat.dis-nn↗
arXiv2023

Robust non-ergodicity of ground state in the $β$ ensemble

In various chaotic quantum many-body systems, the ground states show non-trivial athermal behavior despite the bulk states exhibiting thermalization. Such athermal states play a crucial role in quantum information theory and its applications. Moreover, any generic quantum many-body system in the Krylov basis is represented by a tridiagonal Lanczos Hamiltonian, which is analogous to the matrices from the $β$ ensemble, a well-studied random matrix model with level repulsion tunable via the parameter $β$. Motivated by this, here we focus on the localization properties of the ground and anti-ground states of the $β$ ensemble. Both analytically and numerically, we show that both the edge states demonstrate non-ergodic (fractal) properties for $β\sim\mathcal{O}(1)$ while the typical bulk states are ergodic. Surprisingly, the fractal dimension of the edge states remain three time smaller than that of the bulk states irrespective of the global phase of the $β$ ensemble. In addition to the fractal dimensions, we also consider the distribution of the localization centers of the spectral edge states, their mutual separation, as well as the spatial and correlation properties of the first excited states.

cond-mat.dis-nn↗
arXiv2023

Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase

We study the stability of non-ergodic but extended (NEE) phases in non-Hermitian systems. For this purpose, we generalize a so-called Rosenzweig-Porter random-matrix ensemble (RP), known to carry a NEE phase along with the Anderson localized and ergodic ones, to the non-Hermitian case. We analyze, both analytically and numerically, the spectral and multifractal properties of the non-Hermitian case. We show that the ergodic and the localized phases are stable against the non-Hermitian nature of matrix entries. However, the stability of the fractal phase depends on the choice of the diagonal elements. For purely real or imaginary diagonal potential the fractal phases is intact, while for a generic complex diagonal potential the fractal phase disappears, giving the way to a localized one.

cond-mat.dis-nn↗
arXiv2023

Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices

The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In $d$-dimension the PLRBM are random matrices with algebraic decaying off-diagonal elements $H_{\vec{n}\vec{m}}\sim 1/|\vec{n}-\vec{m}|^α$, having AT at $α=d$. In this work, we investigate the fate of the PLRBM to non-Hermiticity. We consider the case where the random on-site diagonal potential takes complex values, mimicking an open system, subject to random gain-loss terms. We provide an analytical understanding of the model by generalizing the Anderson-Levitov resonance counting technique to the non-Hermitian case. This generalization identifies two competing mechanisms due to non-Hermiticity: one favoring localization and the other delocalization. The competition between the two gives rise to AT at $d/2\le α\le d$. The value of the critical $α$ depends on the strength of the on-site potential, reminiscent of Hermitian disordered short-range models in $d>2$. Within the localized phase, the wave functions are algebraically localized with an exponent $α$ even for $α<d$. This result provides an example of non-Hermiticity-induced localization.

cond-mat.dis-nn↗
arXiv2023

Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder

Models with correlated disorders 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 the others, like the all-to-all translation-invariant Rosenzweig-Porter (TI RP) ensemble or the Hilbert-space structure of the many-body localization, one needs to develop more sophisticated and usually phenomenological methods to find the localization transition. In addition, such models contain not only localization but also the ergodicity-breaking transition, giving way to the non-ergodic extended phase of states with non-trivial fractal dimensions $D_q$. In this work, we suggest a method to calculate both the above transitions and a lower bound to the fractal dimensions $D_2$ and $D_\infty$, relevant for physical observables. In order to verify this method, we apply it to the class of long-range (self-)dual models, interpolating between AA and TI RP ones via both power-law dependences of on-site disorder correlations and hopping terms, 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 fractal phases in an 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.

cond-mat.dis-nn↗