We use the method of bulk-boundary correspondence of topological invariants to show that disordered topological insulators have at least one delocalized state at their boundary at zero energy. Those insulators which do not have chiral (sublattice) symmetry have in addition the whole band of delocalized states at their boundary, with the zero energy state lying in the middle of the band. This result was previously conjectured based on the anticipated properties of the supersymmetric (or replicated) sigma models with WZW-type terms, as well as verified in some cases using numerical simulations and a variety of other arguments. Here we derive this result generally, in arbitrary number of dimensions, and without relying on the description in the language of sigma models.
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.
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 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…
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 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.
When a system of spinless fermions in a disordered mesoscopic ring becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the persistent current can be enhanced by orders of magnitude. This is illustrated by a study of the change of the ground state energy under twisted boundary conditions using the density matrix renormalization group algorithm.
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…
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.
In this paper we introduce the spectral approach to delocalization in infinite disordered systems and provide a physical interpretation in context of the classical model of Edwards and Thouless. We argue that spectral analysis is an important contribution to localization problems since it avoids issues related to the use of boundary conditions. Applying the method to 2D and 3D numerical simulations with various amount of disorder W shows that delocalization occurs for W<=0.6 in 2D and for W<=5 for 3D.
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…
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 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…
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…
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…
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…
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.
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…
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…
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…
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…
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 …
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 …
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown prove that extended states exist for disordered honeycomb, triangular, and square crystals. This observation stands in contrast to the predictions of scaling theory, and aligns with experiments in photonic lattices and electron systems. The method used is the only theoretical approach aimed at showing delocalization. A comparison of the results for the three g…
We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a F…
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…
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…
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…
We report exact multielectronic ground-states dependent on electron concentration for quantum mechanical two-dimensional disordered two-band type many body models in the presence of disordered hoppings and disordered repulsive finite Hubbard interactions, in fixed lattice topology considered provided by Bravais lattices. The obtained ground-states loose their eigenfunction character for independent electron approximation, perturbatively are not connected to the non-interacting but disordered case, and describe a localization-delocalization transition driven by the electron concentration, being…
We calculate the corrections to the conductivity and compressibility of a disordered metal when the mean free path is smaller than the screening length. Such a condition is shown to be realized for low densities and large disorder. Analysis of the stability of the metallic state reveals a transition to the insulating state in two-dimensions.
We study how interacting localized degrees of freedom are affected by slow thermal fluctuations that change the effective local disorder. We compute the time-averaged (annealed) conductance in the insulating regime and find three distinct insulating phases, separated by two transitions. The first occurs between a non-resonating insulator and an intermittent metal. The average conductance is always dominated by rare temporal fluctuations. However, in the intermittent metal, they are so strong that the system becomes metallic for an exponentially small fraction of the time. A second transition o…
We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase which is stabilized by electronic interactions, from the insulating phase where disorder prevails over the electronic interactions, has been identified. The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached. We show that the interplay of electron-electron interac…
The phase diagram of correlated, disordered electrons is calculated within dynamical mean--field theory using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases, as well as coexistence and crossover regimes are identified. The Mott and Anderson insulators are found to be continuously connected.
Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is however nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit, but are challenging for models without translational invariance. Here, we demonstrate that NLCE provide a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$…
The interplay between interaction, disorder, and dissipation has shown a rich phenomenology. Here we investigate a disordered XXZ spin chain in contact with a bath which, alone, would drive the system towards a highly delocalized and coherent Dicke state. We show that there exist regimes for which the natural orbitals of the single-particle density matrix of the steady state are all localized in the presence of strong disorders, either for weak interaction or strong interaction. We show that the averaged steady-state occupation in the eigenbasis of the open system Hamiltonian could follow an e…
We study one-dimensional disordered fermions that either undergo metal-insulator transitions or topological phase transitions to become trivial Anderson insulators. We focus on using entanglement to elucidate how the spatial, momentum, and internal degrees of freedom of fermions are affected by the presence of disorder in such cases. We develop entanglement tools that reveal the existence of metallic states in the presence of disorder and further show clear signatures of the corresponding localization transition even in the presence of interactions. In systems where the internal degrees of fre…
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。
We use the dynamical mean-field approximation to study singularities in the self-energy and a two-particle irreducible vertex induced by the metal-insulator transition of the disordered Falicov-Kimball model. We set general conditions for the existence of a critical metal-insulator transition caused by a divergence of the imaginary part of the self-energy. We calculate explicitly the critical behavior of the self-energy for the symmetric and asymmetric disorder distributions. We demonstrate that the metal-insulator transition is preceded by a pole in a two-particle irreducible vertex. We show …
Anderson and dynamical localization have been experimentally observed with ultra-cold atomic matter. Feshbach resonances are used to efficiently control the strength of interactions between atoms. This allows to study the delocalization effect of interactions for localized wave packets. The delocalization processes are subdiffusive and slow, thereby limiting the quantitative experimental and numerical analysis. We propose an elegant solution of the problem by proper ramping the interaction strength in time. We demonstrate that subdiffusion is speeded up to normal diffusion for interacting diso…
We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization and the local bond conductivity, we find a collapse of the Mott gap toward a V-shape pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites but an increase of bond conductivity. These metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Bond conducti…
We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement…
We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically we consider one-dimensional stub and two-dimensional kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, $h$. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with $h$, in contrast to the dispersive-ba…
In a one-dimensional (1D) disordered potential, quantum interferences leading to Anderson lo-calization are ubiquitous, such that all wave-functions are exponentially localized. Moreover, no phase transition toward delocalization is expected in 1D. This behavior is strongly modified in the presence of a bias force. We experimentally study this case, launching a non-interacting 39 K Bose-Einstein condensate in a 1D disordered potential induced by a far-off-resonance laser speckle, while controlling a bias force. In agreement with theoretical predictions, we observe a transition between algebrai…
We present an asymptotically exact renormalization-group theory of the superfluid--insulator transition in one-dimensional disordered systems, with emphasis on an accurate description of the interplay between the Giamarchi--Schulz (instanton--anti-instanton) and weak-link (scratched-XY) criticalities. Combining the theory with extensive quantum Monte Carlo simulations allows us to shed new light on the ground-state phase diagram of the one-dimensional disordered Bose-Hubbard model at unit filling.
We investigate the presence of percolating states in disordered two-dimensional topological insulators. In particular, we uncover a close connection between these states and the so-called topological Anderson insulator (TAI), which is a topologically non-trivial phase induced by the presence of disorder. The decay of this phase could previously be connected to a delocalization of bulk states with increasing disorder strength. In this work we identify this delocalization to be the result of a percolation transition of states that circumnavigate the hills of the bulk disorder potential.
A weakly disordered quasi-one-dimensional tight-binding hopping model with $N$ rows is considered. The probability distribution of the Landauer conductance is calculated exactly in the middle of the band, $ε=0$, and it is shown that a delocalization transition at this energy takes place if and only if $N$ is odd. This even-odd effect is explained by level repulsion of the transmission eigenvalues.
While global quantum quench has been extensively used in the literature to understand the localization-delocalization transition for the one-dimensional quantum spin chain, the effect of geometric quench (which corresponds to a sudden change of the geometry of the chain) in the context of such transitions is yet to be well understood. In this work, we investigate the effect of geometric quench in the Aubry-Andre model, which supports localization-delocalization transition even in one dimension. We study the spreading of the entanglement and the site-occupation with time and find many interesti…
We consider the many-body localization-delocalization transition for strongly interacting one- dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transitions at any finite temperature when varying the interaction strength. At weak interactions an increase in the interaction strength leads to insulator->fluid transition, and for large interactions one has a reentrance to the insulator regime.
We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder $W_c(L, d)$ as a function of length $L$ and width $d$. In the quasi-1D case $W_c$ has a finite large-$L$ limit at fixed $d$, which increases strongly with $d$. In the 2D case $W_c(L,L)$ grows with $L$. The results are consistent with th…
The universality of the metal-insulator transition in three-dimensional disordered system is confirmed by numerical analysis of the scaling properties of the electronic wave functions. We prove that the critical exponent $ν$ and the multifractal dimensions $d_q$ are independent on the microscopic definition of the disorder and universal along the critical line which separates the metallic and the insulating regime.
We calculate self-consistently the mutual dependence of electron correlations and electron-defect scattering for a two dimensional electron gas at finite temperature. We employ an STLS approach to calculate the electron correlations while the electron scattering rate off Coulombic impurities and surface roughness is calculated using self-consistent current-relaxation theory. The methods are combined and self-consistently solved. We discuss a metal-insulator transition for a range of disorder levels and electron densities. Our results are in good agreement with recent experimental observations.
We are interested in the out of equilibrium phenomena observed in the electrical conductance of disordered insulators at low temperature, which may be signatures of the electron coulomb glass state. The present work is devoted to the occurrence of ageing, a benchmark phenomenon for the glassy state. It is the fact that the dynamical properties of a glass depend on its age, i.e. on the time elapsed since it was quench-cooled. We first critically analyse previous studies on disordered insulators and question their interpretation in terms of ageing. We then present new measurements on insulating …
Localization of wavefunctions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [[V. Khemani, R. Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary to naive expectation, manipulation of a localized-site in the disordered medium may produce a disturbance over a length-scale much larger than the localization-length $ξ$. Here we report on the observation of this nonlocal phenomenon in electronic transport experiment. Being a wave property, visibility of this effect hinges upon quantum-coherence, and its spatial-scale may be…
