We consider a one-dimensional quantum many-body system and investigate how the interplay between interaction and on-site disorder affects spatial localization and quantum correlations. The hopping amplitude is kept constant. To measure localization, we use the number of principal components (NPC), which quantifies the spreading of the system eigenstates over vectors of a given basis set. Quantum correlations are determined by a global entanglement measure $Q$, which quantifies the degree of entanglement of multipartite pure states. Our studies apply analogously to a one-dimensional system of interacting spinless fermions, hard-core bosons, or yet to an XXZ Heisenberg spin-1/2 chain. Disorder is characterized by both: uncorrelated and long-range correlated random on-site energies. Dilute and half-filled chains are analyzed. In half-filled clean chains, delocalization is maximum when the particles do not interact, whereas multi-partite entanglement is largest when they do. In the presence of uncorrelated disorder, NPC and Q show a non-trivial behavior with interaction, peaking in the chaotic region. The inclusion of correlated disorder may further extend two-particle states, but the effect decreases with the number of particles and strength of their interactions. In half-filled chains with large interaction, correlated disorder may even enhance localization.
In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states based on the normalized localization length by controlling the correlation and the disorder strength of the potential. In addition, the transition of the diffusive property of wavepacket dynamics is shown around the critical point.
Quantum effects on the atom delocalization in amorphous silicon have been studied by path-integral Monte Carlo simulations from 30 to 800 K. The quantum delocalization is appreciable vs. topological disorder, as seen from structural observables such as the radial distribution function (RDF). At low temperatures, the width of the first peak in the RDF increases by a factor of 1.5 due to quantum effects. The overall anharmonicity of the solid vibrations at finite temperatures in amorphous silicon is clearly larger than in the crystalline material. Low-energy vibrational modes are mainly located …
In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88, 264]. In the present work, we study the energy ($E \neq 0$) dependence of the normalized localization length and the delocalization of the wavefunction at the different energy in the same system. The mobility edges in the LDT arise when the fractal dimension of the potential landscape is larger than the critical value depending on the disorder strength, whic…
The localization in a disordered system of $N$ interacting spins coupled by the long-range anisotropic interaction $1/R^α$ is investigated using a finite size scaling in a $d=1$ -dimensional system for $N=8, 10, 12, 14$. The results supports the absence of localization in the infinite system at $α<2d$ and a scaling of a critical energy disordering $W_{c} \propto N^{2d-α}$ in agreement with the analytical theory suggesting the energy delocalization in the subset of interacting resonant pairs of spins as a precursor of the many-body delocalization.The spin relaxation rate $k$ dependence on disor…
A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to localized state always occurs as the perturbation strength is weakened below a critical value. The nature of the transition qualitatively follows the Anderson transition (AT) if the number of degrees of freedom $M+1$ is regarded as the spatial dimension $d$, but the critical dimension is not $d=M+1-2$ of the ordinary AT but $d=3$.
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of $ν= 1.550^{+0.020}_{-0.017}$ confirms the agreement with the universality class of the standard electronic Anderson m…
Based on the random dimer model, we study correlated disorder in a one dimensional system driven by a strong AC field. As the correlations in a random system may generate extended states and enhance transport in DC fields, we explore the role that AC fields have on these properties. We find that similar to ordered structures, AC fields renormalize the effective hopping constant to a smaller value, and thus help to localize a state. We find that AC fields control then a localization-delocalization transition in a given one dimensional systems with correlated disorder. The competition between ba…
Localization-delocalization transition in a discrete Anderson nonlinear Schrödinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity parameter thought as the control parameter. In vicinity of the critical point the spreading of the wave field is subdiffusive in the limit $t\rightarrow+\infty$. The second moment grows with time as a powerlaw $\propto t^α$, with $α$ exactly 1/3. This critical spreading finds its significance in some connection with the general problem of transport along separatrices…
The localization behavior of the one-dimensional Anderson model with correlated and uncorrelated purely off-diagonal disorder is studied. Using the transfer matrix method, we derive an analytical expression for the localization length at the band center in terms of the pair correlation function. It is proved that for long-range correlated hopping disorder, a localization-delocalization transition occurs at the critical Hurst exponent H_c= 1/2 when the variance of the logarithm of hopping "σ_{\ln(t)}" is kept fixed with the system size N. Based on numerical calculations, finite size scaling rel…
Continuous One-dimensional models supporting extended states are studied. These delocalized statesoccur at well defined values of the energy and are consequences of simple statistical correlation rules. We explicitly study alloys of delta-barrier potentials as well as alloys and liquids of quantum well as.The divergence of the localization length is studied and a critical exponent 2/3 is found for the delta-barrier case, whereas for the quantum wells we find an exponent of 2 or 2/3 depending on the well's parameters. These results support the idea that correlations between random scattering se…
It is well-known that disordered quantum magnets usually host localized elementary excitations in gapped phases. Here we show that long-range magnetodipolar interaction can lead to quasiparticles delocalization in the three-dimensional case, similarly to the phenomenon previously described for localized vibrational modes in disordered solids. Employing renormalization group-like ideas, the average eigenmode occupation number is found to scale with the system size, which also leads to sub-diffusive dynamical properties of the system.
We investigate localization properties of electron eigenstates in one-dimensional (1d) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $ξ$ of eigenstates demonstrate the existence of the localization-delocalization transition in 1d systems and elucidate non-trivial behavior of $ξ$ as a function of the disorder strength. The critical exponent $ν$ for localization length is extracted for various values of parameters characterizing the disorder, revealing that every $ν$ disobeys the Harris criterion $ν> 2/d$.
We study delocalization transition in a one-dimensional electron system with quenched disorder by using supersymmetric (SUSY) methods. Especially we focus on effects of nonlocal correlation of disorder, for most of studies given so far considered $δ$-function type white noise disorder. We obtain wave function of the "lowest-energy" state which dominates partition function in the limit of large system size. Density of states is calculated in the scaling region. The result shows that delocalization transition is stable against nonlocal short-ranged correlation of disorder. Especially states near…
Uncorrelated disorder in generalized 3D Lieb models gives rise to the existence of bounded mobility edges, destroys the macroscopic degeneracy of the flat bands and breaks their compactly-localized states. We now introduce a mix of order and disorder such that this degeneracy remains and the compactly-localized states are preserved. We obtain the energy-disorder phase diagrams and identify mobility edges. Intriguingly, for large disorder the survival of the compactly-localized states induces the existence of delocalized eigenstates close to the original flat band energies -- yielding seemingly…
We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and {\it non-random} long-range inter-site interaction $J_{mn}=J/|m-n|^μ$. The model is critical at $1<μ<3/2$ and reveals the localization-delocalization transition with respect to the disorder magnitude. To detect the transition we analyze level and wave function statistics. It is demonstrated also that in the marginal case ($μ= 3/2$) all states are localized.
We study effects of weak nonlineary on localization of waves in disordered Stark ladder corresponding to propagation in presence of disorder and a static field. Our numerical results show that nonlinearity leads to delocalization with subdiffusive spreading along the ladder. The exponent of spreading remains close to its value in absence of the static field.
Spectral Topology and Delocalization in Disordered Hatano-Nelson Chains
Department of Physics, Siksha-Bhavana, Visva-Bharati（维沙-巴拉提大学物理系）；Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS)（基础科学研究院复杂系统理论物理中心）；Basic Science Program, Korea University of Science and Technology (UST)（韩国科学技术院基础科学项目）；Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study (NZIAS), Massey University Albany（梅西大学阿尔巴尼新西兰高级研究院理论与化学物理中心）
研究无序Hatano-Nelson链的安德森局域化特性，发现弱 disorder 时谱形成单环，临界 disorder 时分裂为两环，谱 winding number 从1变为1/2再变为0，证明态子指数局域化，且弱和临界 disorder 时存在完全局域化的态。
The interplay of disorder and spin-fluctuation effects in a disordered antiferromagnet is studied. In the weak-disorder regime (W \le U), while the energy gap decreases rapidly with disorder, the sublattice magnetization, including quantum corrections, is found to remain essentially unchanged in the strong correlation limit. Magnon energies and Neel temperature are enhanced by disorder in this limit. A single paradigm of disorder-enhanced delocalization qualitatively accounts for all these weak disorder effects. Vertex corrections and magnon damping, which appear only at order (W/U)^4, are als…
We present electrical transport measurements in natural graphite and highly ordered pyrolytic graphite (HOPG), comparing macroscopic samples with exfoliated, nanofabricated specimens of nanometer thickness. The latter exhibit a very large c-axis resistivity $ρ_c$ -- much larger than expected from simple band theory -- and non-monotonic temperature dependence, similar to macroscopic HOPG, but in stark contrast to macroscopic natural graphite. A recent model of disorder-induced delocalization is consistent with our transport data. Furthermore, Micro-Raman spectroscopy reveals clearly reduced dis…
We study the localization properties of disordered semiconductor superlattices driven by ac-fields. The localization length of the electrons in the superlattice increases when the frequency of the driving field is smaller than the miniband width. We show that there is an optimal value of the amplitude of the driving field for which the localization length of the system is maximal. This maximum localization length increases with the inverse of the driving frequency.
We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to dislocation in comparison with the non-relativistic particles with the same disorder strength. More intriguingly, we reveal that the massless Dirac particles are entirely delocalized for any energy due to the inherent chiral symmetry, leading to a well-known result that particles are always localized in one-dimensional system for arbitrary weak disorders to break down. Furthermore, we propose a feasible scheme to simulate and detect the del…
We study theoretically the competition between directional asymmetric coupling and disorder in a one-dimensional array of quantum emitters chirally coupled through a waveguide mode. Our calculation reveals highly nontrivial phase diagram for the eigenstates spatial profile, nonmonotonously depending on the disorder and directionality strength. The increase of the coupling asymmetry drives the transition from Anderson localization in the bulk through delocalized states to chirality-induced localization at the array edge. Counterintuitively, this transition is not smeared by strong disorder but …
We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^α$. We found that for $α< 1$, one-magnon excitations remain exponentially localized with the localization length $ξ$ diverging as 1/E. For $α= 1$ a faster divergence of $ξ$ is obtained. For any $…
The generalization of the dimer model on a two-leg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how…
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the preliminary letter [PRE {\bf 103}, L040202(2021)]. We investigate in detail the localization-delocalization characteristics of the model with respect to three parameters: the disorder strength $W$, the perturbation strength $ε$ and the number of the colors $M$ which plays the similar role of spatial dimension. In particular, attentions are focused on the pr…
We study Anderson localization of massless Dirac electrons in two dimensions in one-dimensional random scalar and vector potentials theoretically for two different cases, in which the scalar and vector potentials are either uncorrelated or correlated. From the Dirac equation, we deduce the effective wave impedance, using which we derive the condition for total transmission and those for delocalization in our random models analytically. Based on the invariant imbedding theory, we also develop a numerical method to calculate the localization length exactly for arbitrary strengths of disorder. In…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^α$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact numerical solutions with a number of spins $N$. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for $d$-dimensional system including the absence of localization in the infinite system at $α<2d$ and a universal scaling of a critical energy disordering $W_{c} \propto N^{\frac{2d-α}{d}}$. %The finite size e…
In the previous paper [PRE 101,032210(2020)], localization and delocalization phenomena in the polychromatically perturbed Anderson map (AM) were elucidated mainly from the viewpoint of localization-delocalization transition (LDT) on the increase of the perturbation strength $ε$. In this paper, we mainly investigate the dependency of the phenomena on the disorder strength $W$ ($W-$dependence) in the AM with a characteristic disorder strength $W^*$. In the completely localized region the $W-$dependence and $ε-$dependence of the localization length show characteristic behavior similar to those r…
We accurately treat the effect of the double and triple interactions of two-level systems (TLS) in glasses onto the energy delocalization due to the long-range interaction of TLS. Although this work qualitatively reproduces the estimates of our previous work we believe that it is important because in this paper the estimates are done with quantitative accuracy. This work can serve as the important step towards the development of quantitative theory of many-body delocalization due to the long-range interaction. Our study is compared with the recent work by Bodea et al claiming that the interact…
The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find th…
Anderson localization1 in a random system is sensitive to a distance dependence of the excitation transfer amplitude V(r). If V(r) decreases with the distance r slower than 1/r^d in a d-dimensional system then all excitations are delocalized at arbitrarily strong disordering, due to the resonant interaction of far separated quantum states (Fig. 1). At finite temperature T>0 the density of excitations is finite and they can influence each other by means of their interaction. Many body excitations involving simultaneous transitions of several single particle excitations create additional channel…
Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and occurs as a result of an interplay between two saddle-points in the free energy functional.
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schrödinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). Nonlinear terms in the equations of motion destroy Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single site, single mode …
The diagrammatic approach is applied to study quasiparticle transport properties in two-dimensional d-wave superconductors with dilute nonmagnetic impurities both in Born and in unitary limits. It is found that a novel quantum interference process gives rise to a weak-antilocalization correction to the spin conductivity, indicating the existence of extended low-energy quasiparticle states. With comimg close to unitarity and the nesting, this correction is suppressed and eventually vanishes due to the global particle-hole symmetry.
A lattice model for disordered d-wave superconductors in class CI is reconsidered. Near the band-center, the lattice model can be described by Dirac fermions with several species, each of which yields WZW term for an effective action of the Goldstone mode. The WZW terms cancel out each other because of the four-fold symmetry of the model, which suggests that the quasiparticle states are localized. If the lattice model has, however, symmetry breaking terms which generate mass for any species of the Dirac fermions, remaining WZW term which avoids the cancellation can derive the system to a deloc…
The effect of Anderson diagonal disorder on the topological surface (``drumhead'') states of a Weyl nodal loop semimetal is addressed. Since diagonal disorder breaks chiral symmetry, a winding number cannot be defined. Seen as a perturbation, the weak random potential mixes the clean exponentially localized drumhead states of the semimetal, thereby producing two effects: (i) the algebraic decay of the surface states into the bulk; (ii) a broadening of the low energy density of surface states of the open system due to degeneracy lifting. This behavior persists with increasing disorder, up to th…
We investigate the localization behavior of electrons in a random lattice which is constructed from a quasi-one-dimensional chain with large coordinate number $Z$ and rewired bonds, resembling the small-world network proposed recently but with site-energy disorder and quantum links instead of classical ones. The random rewiring of bonds in the chain with large $Z$ enhances both the topological disorder and the effective dimensionality. From the competition between disorder and dimensionality enhancement a transition from localization to delocalization is found by using the level statistics met…
Motivated by anomalously large conductivity anisotropy in layered materials, we propose a simple model of randomly spaced potential barriers (mimicking stacking faults) with isotropic impurities in between the barriers. We solve this model both numerically and analytically, by utilizing an exact solution for the conductivity of a one-dimensional (1D) disordered system. In the absence of bulk disorder, electron motion in the out-of-plane direction is localized. Bulk disorder destroys 1D localization. As a result, the out-of-plane conductivity is finite and scales linearly with the scattering ra…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak disorder the interactions reduce spectral correlations and lead to localization, for the case of strong disorder we find that a moderate Coulomb interaction has a delocalizing effect. In addition, we observe a non-universal structure in the level-spacing distribution which we attribute to a mechanism reinforcing spectral correlations taking place in small s…
In disordered two dimensional Chern insulators, a single bulk extended mode is predicted to exist per band, up to a critical disorder strength; all the other bulk modes are localized. This behavior contrasts strongly with topologically trivial two-dimensional phases, whose modes all become localized in the presence of disorder. Using a tight-binding model of a realistic photonic Chern insulator, we show that delocalized bulk eigenstates can be observed in an experimentally realistic setting. This requires the selective use of resonator losses to suppress topological edge states, and acquiring …
As opposed to random disorder, which localizes single-particle wave-functions in 1D at arbitrarily small disorder strengths, there is a localization-delocalization transition for quasi-periodic disorder in the 1D Aubry-André model at a finite disorder strength. On the single-particle level, many properties of the ground-state critical behavior have been revealed by applying a real-space renormalization-group scheme; the critical properties are determined solely by the continued fraction expansion of the incommensurate frequency of the disorder. Here, we investigate the many-particle localizati…
The exact probability distributions of the resistance, the conductance and the transmission are calculated for the one-dimensional Anderson model with long-range correlated off-diagonal disorder at E=0. It is proved that despite of the Anderson transition in 3D, the functional form of the resistance (and its related variables) distribution function does not change when there exists a Metal-Insulator transition induced by correlation between disorders. Furthermore, we derive analytically all statistical moments of the resistance, the transmission and the Lyapunov Exponent. The growth rate of th…
Clarifying the interplay of interactions and disorder is fundamental to the understanding of many quantum systems, including superfluid helium in porous media, granular and thin-film superconductors, and light propagating in disordered media. One central aspect for bosonic systems is the competition between disorder, which tends to localize particles, and weak repulsive interactions, which instead have a delocalizing effect. Since the required degree of independent control of the disorder and of the interactions is not easily achievable in most available physical systems, a systematic experime…
Disorder-enabled directional delocalization and wave steering in time-modulated Dirac materials
Research Institute of Basic Sciences, Ajou University（亚洲大学基础科学研究院）；Department of Physics, Ajou University（亚洲大学物理系）；School of Physics, Korea Institute for Advanced Study（韩国高等研究院物理学院）
The question of whether DNA is intrinsically conducting or not is still a challenge. The ongoing debate on DNA molecules as an electronic material has so far underestimated a key distinction of the system: the role of base pairing (inter chain correlation) in opposition to correlations along each chain. In the present work we show that a disordered double-chain presents truly delocalized states. This effect is irrespective to the sequencing along each chain: DNA-like base pairing reveals to be an efficient delocalization mechanism.
The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at $E_c = ε_{a,b}$ of two possible values of the chemical potential in case of $\midε_a-ε_b\mid \leq 2 $ is confirmed and the corresponding indices of the localization length were calculated. The singular integral equation connecting the density of states with the inverse localization length is solved and the analytic expression for the density of states compared with the numerical calculations.
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for strong disorder and low dimensions. In one dimension and for discrete uncorrelated random potentials, such as tight binding models, all states are localized for any disorder strength. This is in contrast to continuous random potentials, where we show here that regardless of the strength of the random potential, we have delocalization in the limit where the r…
We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in $d<3$, while in $d \geq 3$ there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for $n$-particle bound states in $d$ dimensions when $d+n\geq 4$. Exact calculations of disorder-averaged $n$-particle Greens functions support our hypothesis. In particular, we show that $3$-particle states in $d=1$ with nearest-neighbor repulsion wil…
We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by calculating the transmission coefficient as a function of energy (-2 < E < 2 in units of the hopping integral in the tight-binding Hamiltonian) and disorder, q (probability that a given site of the lattice is not available to the particle). Our study based on finite size scaling suggests the existence of delocalized states that depends on energy and amount of disorde…
Institute for Basic Science (IBS)（基础科学研究院）；Indian Institute of Technology-Kanpur（坎普尔印度理工学院）；Korea University of Science and Technology (UST)（韩国科学技术院）；Massey University（梅西大学）
