Algebraic localization from power-law couplings in disordered quantum wires

Abstract

We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance as a power-law 1/ α . Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a longdistance algebraic decay of correlations within disordered-localized phases, for all exponents α. The exponent of algebraic decay depends only on α, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave-functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular and solid-state physics.Quantum waves are generally localized exponentially by disorder. Following the seminal work by Anderson with spinpolarized electrons [1] much experimental [2-8] and theoretical interest has been devoted to the study of localized phases and to the localization-delocalization transition for non-interacting and interacting quantum models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].While most works have focused on short-range couplings, long-range hopping and interactions that decay with distance as a power-law 1/ α have recently attracted significant interest [29][30][31][32][33][34][35][36][37][38][39][40][41] as they can be now engineered in a variety of atomic, molecular and optical systems. For example, powerlaw spin interactions with tunable exponent 0 < α < 3 can be realized in arrays of laser-driven cold ions [42][43][44][45][46] or between atoms trapped in a photonic crystal waveguide [47-50]; dipolar-type 1/ 3 or van-der-Waals-type 1/ 6 couplings have been experimentally demonstrated with ground-state neutral atoms [51][52][53][54], Rydberg atoms [55-69], polar molecules [70-72] and nuclear spins [73]. In solid state materials, powerlaw hopping is of interest for, e.g., excitonic materials [74][75][76][77][78][79][80][81][82][83][84][85][86], while long-range 1/ coupling is found in helical Shiba chains [87,88], made of magnetic impurities on an s-wave superconductor. In many of these systems, disorder -in particles' positions, local energies, or coupling strengths -is an intrinsic feature, and understanding its effects on singleparticle and many-body localization remains a fundamental open question.For non-interacting models, it is generally expected that long-range hopping induces delocalization in the presence of disorder for α < d, while for α > d all wave-functions are exponentially localized [1,[89][90][91][92]. However, recent theoretical works with positional [93] and diagonal [92] disorder have demonstrated that localization can survive even for α < d. Surprisingly, wave-functions were found to be localized only algebraically in these models, in contrast to the usual Anderson-type exponential localization expected from shortrange models. How these finding translate to the behavior of * davide.vodola@gmail.com † pupillo@unistra.f...

Subradiance-protected excitation transport

“…Finally, we analyze the effect of disorder, which arises from the width of the external wavefunction of the atoms in each lattice trap and is inevitable in a realistic experimental scenario. Even though this can lead to the suppression of the transport of the wave packet due to localization [47,48], we find that the subradiant character of the dynamics is robust against the presence of disorder [49,50].…”

Correlation-induced localization

“…Finally, the most challenging problem motivated by our paper is the effect of correlations on Many Body Localization in the long-range interacting models (see, e.g., [15][16][17][18][19][20][21][22][23][24][25][26][27]…”

“…Several models with such interactions have been suggested in the past [15] and recently [16][17][18][19][20][21][22][23][24][25][26][27] in the problem of entanglement dynamics at many-body localization. The models with fully-correlated hopping and interaction terms [15,16,18,[21][22][23][24]26] show significantly different behavior as compared to the ones with uncorrelated hopping and interactions [16,17,19,25,27]. Some of the former works (see, e.g., [23]) even demonstrate explicitly that manybody properties are formed as superpositions of short-range and power-law decaying contributions in the complete agreement with the single-particle picture developed in this work.…”

Many-body localization in presence of cavity mediated long-range interactions

“…In recent works [11] it was argued that MBL may appear in disordered long-range interacting systems, others suggest [12][13][14][15] lack of MBL for, e.g., dipole-dipole interactions in three dimensions (3D) [16,17]. Furthermore, MBL in presence of power-law decaying tunneling elements and interactions has been studied in [18][19][20] where algebraic decay of correlation functions as well as of algebraic growth of entanglement entropy was found. In other studies [21][22][23][24] a model of a single spin coupled to all sites of otherwise short-range interacting systems was analysed showing that the presence of additional coupling may strongly modify MBL properties.…”