Elementary Excitations in the Fermi Glass

Fleǐshman, L. S.; Licciardello, D.C.; Anderson, Philip W.

doi:10.1103/physrevlett.40.1340

Cited by 71 publications

(47 citation statements)

References 8 publications

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“…The presence of inelastic scattering, such as is caused by electron-phonon interactions, leads to hopping of electrons between localized states and gives rise to a finite conductivity. The question as to whether electron-electron interactions lead to a similar effect has attracted much attention recently but is still not fully understood [146,147,148,149,150,151,152]. The main interest is to understand the transition, from an insulating state governed by the physics of Anderson localization, to a conducting state as one increases interactions.…”

Section: Systems With Disorder and Interactionsmentioning

confidence: 99%

Heat transport in low-dimensional systems

Dhar

2008

Advances in Physics

923

1,114

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Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet nontrivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard particle and hard disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green-Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ, diverges with system size L, as κ ∼ L α . For one dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given. IntroductionIt is now about two hundred years since Fourier first proposed the law of heat conduction that goes by his name. Consider a macroscopic system subjected to different temperatures at its boundaries. One assumes that it is possible to have a * Corresponding author. Email: dabhi@rri.res.in November 19, 2008 19:56 Advances in Physics reva 2 coarse-grained description with a clear separation between microscopic and macroscopic scales. If this is achieved, it is then possible to define, at any spatial point x in the system and at time t, a local temperature field T (x, t) which varies slowly both in space and time (compared to microscopic scales). One then expects heat currents to flow inside the system and Fourier argued that the local heat current density J(x, t) is given bywhere κ is the thermal conductivity of the system. If u(x, t) represents the local energy density then this satisfies the continuity equation ∂u/∂t + ∇.J = 0. Using the relation ∂u/∂T = c, where c is the specific heat per unit volume, leads to the heat diffusion equation:Thus, Fourier's law implies diffusive transfer of energy. In terms of a microscopic picture, this can be understood in terms of the motion of the heat carriers, i.e. , molecules, electrons, lattice vibrations(phonons), etc., which suffer random collisions and hence move diffusively. Fourier's law is a phenomological law and has been enormously succesful in providing an accurate description of heat transport phenomena as observed in experimental systems. However there is no rigorous derivation of this law starting from a microscopic Hamiltonian description and this basic question has motivated a large number of studies on heat conduction in model systems. One important and somewhat surprising conclusion that emerges from these studies is that Fourier's law is probably not valid in one and two dimensional systems, except when the ...

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Section: Systems With Disorder and Interactionsmentioning

confidence: 99%

Heat transport in low-dimensional systems

Dhar

2008

Advances in Physics

923

1,114

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“…Anderson localized systems are, however, non-generic, since they do not include interactions which allow for the exchange of energy. For many years it was assumed that interactions generally restore ergodicity and destroy localization [2]. A decade ago, using non-equilibrium diagrammatic techniques, it was argued that Anderson localization is stable under the addition of a small shortranged interactions [3], a phenomenon currently known as many-body localization (MBL).…”

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confidence: 99%

Many-body localization in system with a completely delocalized single-particle spectrum

2016

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Many-body localization (MBL) in a one-dimensional Fermi Hubbard model with random on-site interactions is studied. While for this model all single-particle states are trivially delocalized, it is shown that for sufficiently strong disordered interactions the model is many-body localized. It is therefore argued that MBL does not necessary rely on localization of the single-particle spectrum. This model provides a convenient platform to study pure MBL phenomenology, since Anderson localization in this model does not exist. By examining various forms of the interaction term a dramatic effect of symmetries on charge transport is demonstrated. A possible realization in a cold atom experiments is proposed. Introduction.-It has been known for almost 60 years that non-interacting particles in one-dimensional disordered systems exhibit Anderson localization [1]. Transport in these systems is exponentially suppressed with the system size, and without coupling to the environment, these systems are non-ergodic at any temperature. Anderson localized systems are, however, non-generic, since they do not include interactions which allow for the exchange of energy. For many years it was assumed that interactions generally restore ergodicity and destroy localization [2]. A decade ago, using non-equilibrium diagrammatic techniques, it was argued that Anderson localization is stable under the addition of a small shortranged interactions [3], a phenomenon currently known as many-body localization (MBL). Many-body localized systems are the only known generic non-ergodic systems which do not follow the assumptions of statistical mechanics [4][5][6]. While the realization of MBL systems presents challenges in condensed matter systems due to inevitable presence of phonons [7,8], recent experiments in cold atoms have provided evidence of the existence of MBL in both one-dimensional [9-11] and two-dimensional systems [12].

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“…For definiteness, we concentrate on the case of a many-channel 1D system with a short-range interaction. Our results are, however, more general (including single-channel wires, 2D systems, Coulomb interaction), as we discuss in the end of the paper.It was proposed in [9] that the e-e interaction by itself is sufficient to induce VRH at low T . This idea was widely used for interpretation of experimental [8,10] and numerical [11] results on 2D systems.…”

mentioning

confidence: 99%

“…It was proposed in [9] that the e-e interaction by itself is sufficient to induce VRH at low T . This idea was widely used for interpretation of experimental [8,10] and numerical [11] results on 2D systems.…”

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confidence: 99%

Interacting Electrons in Disordered Wires: Anderson Localization and Low-TTransport

2005

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We study transport of interacting electrons in a low-dimensional disordered system at low temperature T . In view of localization by disorder, the conductivity σ(T ) may only be non-zero due to electron-electron scattering. For weak interactions, the weak-localization regime crosses over with lowering T into a dephasing-induced "power-law hopping". As T is further decreased, the Anderson localization in Fock space crucially affects σ(T ), inducing a transition at T = Tc, so that σ(T < Tc) = 0. The critical behavior of σ(T ) above Tc is ln σ(T ) ∝ −(T − Tc) −1/2 . The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space. 72.15.Rn, 71.30.+h, In a pathbreaking paper [1] Anderson demonstrated that a quantum particle may become localized by a random potential. In particular, in non-interacting systems of one-dimensional (1D) or two-dimensional (2D) geometry even weak disorder localizes all electronic states [2], thus leading to the exactly zero conductivity, σ(T ) = 0, whatever temperature T . A non-zero σ(T ) in such systems may only occur due to inelastic scattering processes leading to dephasing of electrons. Two qualitatively different sources of dephasing are possible: (i) scattering of electrons by external excitations (in practice, phonons) and (ii) electron-electron (e-e) scattering. In either case, at sufficiently high temperatures, the dephasing rate τ −1 φ is high, so that the localization effects are reduced to a weak-localization (WL) correction to the Drude conductivity. This correction behaves as ln τ φ in 2D and as τ 1/2 φ in quasi-1D (many-channel wire) systems [3], and thus diverges with lowering T , signaling the occurrence of the strong localization (SL) regime. This prompts a question as to how the system conducts at low T .For the case of electron-phonon scattering the answer is well known. The conductivity is then governed by Mott's variable-range hopping (VRH) [4], yielding σ(T ) ∝ exp{−(T 0 /T ) µ } with µ = 1/(d+1), where d is the spatial dimensionality. In the presence of a long-range Coulomb interaction, the Coulomb gap in the tunneling density of states modifies the VRH exponent, µ = 1 2 [5]. But what is the low-T behavior of σ(T ) if the electronphonon coupling is negligibly weak and the only source of the inelastic scattering is the e-e interaction? Our purpose here is to solve this long-standing fundamental problem, which is also of direct experimental relevance; see, e.g., Refs.[6] and [7,8], where the crossover from WL to SL with lowering T was studied for 1D and 2D systems, respectively. For definiteness, we concentrate on the case of a many-channel 1D system with a short-range interaction. Our results are, however, more general (including single-channel wires, 2D systems, Coulomb interaction), as we discuss in the end of the paper.It was proposed in [9] that the e-e interaction by itself is sufficient to induce VRH at low T . This idea was widely used for interpretation of experimental [8,10] and numerical [11] results on ...

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Elementary Excitations in the Fermi Glass

Cited by 71 publications

References 8 publications

Heat transport in low-dimensional systems

Heat transport in low-dimensional systems

Many-body localization in system with a completely delocalized single-particle spectrum

Interacting Electrons in Disordered Wires: Anderson Localization and Low-TTransport

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