Anderson-Hubbard model with box disorder: Statistical dynamical mean-field theory investigation

Semmler, D.; Byczuk, Krzysztof; Hofstetter, Walter

doi:10.1103/physrevb.84.115113

Cited by 36 publications

(25 citation statements)

References 68 publications

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“…A similar linear increase of the critical quasi-disorder for weak repulsion was previously obtained for the Aubry-André model within the self-consistent Hartree-Fock approximation [40]; also the statistical dynamical mean-field theory of Ref. [46] predicts delocalizing effects due to repulsive interaction. It is likely that this linear increase would cease to hold for strong interactions γ 1; this regime is however beyond the scope of this work.…”

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confidence: 78%

Localization of interacting Fermi gases in quasiperiodic potentials

Pilati

Varma

2017

Phys. Rev. A

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We investigate the zero-temperature metal-insulator transition in a one-dimensional twocomponent Fermi gas in the presence of a quasi-periodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low energy) Anderson localized and (high energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasi-periodic potential. In order to discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point. To what extent, if at all, do Anderson insulators persist in the presence of interactions? This has been an outstanding problem since 1958 when noninteracting quantum systems were theoretically shown by Anderson to harbor no transport of conserved quantities for sufficiently strong disorder [1,2]. In cold atom settings, among others, experimenters have observed the Anderson transition of noninteracting particles either in the nondeterministic random disorder created using spatiallycorrelated speckle patterns or in the one-dimensional quasidisorder created using incommensurate bichromatic lattice [3][4][5][6][7]. Theoretical predictions about the critical point of the Anderson transition based on models that take into account the details of these cold-atoms experiments have been recently reported [8][9][10][11], enabling quantitative comparison with experimental measurements [12].Cold-atoms experiments have emerged as the ideal playground to explore also the effects due to interactions in disordered many-body systems [13,14]. Experiments to understand the transport and localization phenomena in disordered interacting atomic gases continue to be performed [15][16][17][18][19][20][21][22]. Theoretically, a decade ago Basko and collaborators showed using diagrammatic techniques that the Anderson insulator can survive in the presence of interactions [23], even at finite temperatures. For continuous-space disordered bosons this finitetemperature localization [24] connects, in the zero temperature limit, to the superfluid to Bose glass transition [25]. The concomitant zero-temperature localization transition for continuous-space weakly interacting quasidisordered fermions is the subject of our study.In this Rapid Communication, we investigate the zero-temperature metal-...

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Section: Fig 4: (Color Online)supporting

confidence: 78%

Localization of interacting Fermi gases in quasiperiodic potentials

Pilati

Varma

2017

Phys. Rev. A

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“…The generalization Equation (A1) was obtained by requiring the known exact asymptotic dependence of the self-energy on frequency in the limit of large frequencies (for details, see [37,63]). The approximation was used by different groups and, despite its limitations, led to encouraging results, even in the case of systems with reduced dimensionality (see, e.g., [64,65]). …”

Section: Discussionmentioning

confidence: 99%

Towards TDDFT for Strongly Correlated Materials

2016

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Abstract:We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch-Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO 3 . We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO 3 , a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response.

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“…To overcome these limitations, DMFT was extended to describe spatially nonuniform systems, in approaches sometimes called "Statistical DMFT" [5][6][7][8][9][10][11][12][13][14][15][16] (some authors call the same approach "Real-Space DMFT" [17][18][19] ). Here, the local DMFT order parameters (i.e.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality at the Anderson transition: A typical medium theory perspective

Mahmoudian¹,

Tang²,

Dobrosavljević³

2015

Phys. Rev. B

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We present a complete analytical and numerical solution of the Typical Medium Theory (TMT) for the Anderson metal-insulator transition. This approach self-consistently calculates the typical amplitude of the electronic wave-functions, thus representing the conceptually simplest order-parameter theory for the Anderson transition. We identify all possible universality classes for the critical behavior, which can be found within such a meanfield approach. This provides insights into how interaction-induced renormalizations of the disorder potential may produce qualitative modifications of the critical behavior. We also formulate a simplified description of the leading critical behavior, thus obtaining an effective Landau theory for Anderson localization.

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Anderson-Hubbard model with box disorder: Statistical dynamical mean-field theory investigation

Cited by 36 publications

References 68 publications

Localization of interacting Fermi gases in quasiperiodic potentials

Localization of interacting Fermi gases in quasiperiodic potentials

Towards TDDFT for Strongly Correlated Materials

Quantum criticality at the Anderson transition: A typical medium theory perspective

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