Duality in Power-Law Localization in Disordered One-Dimensional Systems

Deng, Xiaolong; Kravtsov, V. E.; Shlyapnikov, G. V.; Santos, Luís

doi:10.1103/physrevlett.120.110602

Cited by 72 publications

(129 citation statements)

References 35 publications

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“…Since the long-ranged exchange interactionsV (given by (3)) are functions of the separation between the atoms, the uncertainty in the atomic positions translates into disorder in the hopping rates in the exchange Hamiltonian H given by equation (2). This kind of positional disorder in Hamiltonians with long-ranged hopping has been recently studied and found to give rise to localization [47]. Consistently with this, we find that as we increase σ the eigenstates of the Hamiltonian become localized, inhibiting transport.…”

Section: Disordersupporting

confidence: 88%

“…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].…”

Section: Introductionmentioning

confidence: 81%

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Subradiance-protected excitation transport

2019

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We explore excitation transport within a one-dimensional chain of atoms where the atomic transition dipoles are coupled to the free radiation field. When the atoms are separated by distances smaller or comparable to the wavelength of the transition, the exchange of virtual photons leads to the transport of the excitation through the lattice. Even though this is a strongly dissipative system, we find that the transport is subradiant, that is, the excitation lifetime is orders of magnitude longer than the one of an individual atom. In particular, we show that a subspace of the spectrum is formed by subradiant states with a linear dispersion relation, which allows for the dispersionless transport of wave packets over long distances with virtually zero decay rate. Moreover, the group velocity and direction of the transport can be controlled via an external uniform magnetic field while preserving its subradiant character. The simplicity and versatility of this system, together with the robustness of subradiance against disorder, makes it relevant for a range of applications such as lossless energy transport and long-time light storage.

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Section: Disordersupporting

confidence: 88%

Section: Introductionmentioning

confidence: 81%

Subradiance-protected excitation transport

2019

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“…with respect to the critical point a = d observed for d = 1 in [32]. The latter model will be discussed in details in Sec.…”

Section: Equation For Effective Chargesmentioning

confidence: 95%

“…The randomness in the model is given both by the off-diagonal elements through the positions of sites r i uniformly distributed in d-dimensional cube with the mean density equal to unity, and by the random bare on-site energies ε i with zero mean, dependent or independent of f (r) and r i . In particular, ε i could be even all equal to zero, as in the power-law Euclidean (PLE) model considered in [32] with d = 1 and f (r) = r −a . Unlike the models with translation-invariant hopping and only diagonal disorder [35][36][37]53], the above model does not necessarily have a small parameter, and, hence, the approximation of the single resonances does not necessarily applicable from the first steps of RG.…”

Section: Renormalization Group Approach 21 Main Ideamentioning

confidence: 99%

Renormalization to localization without a small parameter

Kutlin

Khaymovich

2020

SciPost Phys.

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We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to generality of this model usually called Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translationinvariant long-range lattice models with a diagonal disorder.

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“…Recent results show that while dipolar interactions in three dimensions can lead to extended states, such systems exhibit non-ergodic behviour [70]. Moreover, algebraic localization (as opposed to exponential Anderson localization) arises in systems with offdiagonal disorder in the long-range spin flip-flop interactions in one dimension [71]. Thus, in a model like equation (8), with a mixture of diagonal and off-diagonal disorder, we might expect to find some form of localization in the single-excitation limit.…”

Section: Single-particle Problemmentioning

confidence: 99%

Many-body physics with ultracold plasmas: quenched randomness and localization

Sous

Grant

2019

New J. Phys.

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The exploration of large-scale many-body phenomena in quantum materials has produced many important experimental discoveries, including novel states of entanglement, topology and quantum order as found for example in quantum spin ices, topological insulators and semimetals, complex magnets, and high-T c superconductors. Yet, the sheer scale of solid-state systems and the difficulty of exercising exacting control of their quantum mechanical degrees of freedom limit the pace of rational progress in advancing the properties of these and other materials. With extraordinary effort to counteract natural processes of dissipation, precisely engineered ultracold quantum simulators could point the way to exotic new materials. Here, we look instead to the quantum mechanical character of the arrested state formed by a quenched ultracold molecular plasma. This novel class of system arises spontaneously, without a deliberate engineering of interactions, and evolves naturally from statespecified initial conditions, to a long-lived final state of canonical density, in a process that conflicts with classical notions of plasma dissipation and neutral dissociation. We take information from experimental observations to develop a conceptual argument that attempts to explain this state of arrested relaxation in terms of a minimal phenomenological model of randomly interacting dipoles of random energies. This model of the plasma forms a starting point to describe its observed absence of relaxation in terms of many-body localization (MBL). The large number of accessible Rydberg and excitonic states gives rise to an unconventional web of many-body interactions that vastly exceeds the complexity of MBL in a conventional few-level scheme. This experimental platform thus opens an avenue for the coupling of dipoles in disordered environments that will demand the development of new theoretical tools.

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Duality in Power-Law Localization in Disordered One-Dimensional Systems

Cited by 72 publications

References 35 publications

Subradiance-protected excitation transport

Subradiance-protected excitation transport

Renormalization to localization without a small parameter

Many-body physics with ultracold plasmas: quenched randomness and localization

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