Analytical properties of polaron systems or: Do polaronic phase transitions exist or not?

Gerlach, B.; Löwen, Hartmut

doi:10.1103/revmodphys.63.63

Cited by 228 publications

(190 citation statements)

References 204 publications

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“…In many models of EPI the ground-state polaron energy is an analytical function of the coupling constant for any dimensionality of space (Fehske and Trugman , 2007;Gerlach and Löwen , 1991;Hague et al , 2006a;Löwen , 1988;Peeters and Devreese , 1982). There is no abrupt (nonanalytical) phase transition of the ground state as the electron-phonon coupling increases.…”

Section: Continuum Polaronmentioning

confidence: 99%

Fröhlich polaron and bipolaron: recent developments

2009

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It is remarkable how the Fröhlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ∼ 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article reviews recent developments in the field of continuum and discrete (lattice) Fröhlich (bi)polarons starting with the basics and covering a number of active directions of research. * Electronic address: jozef.devreese@ua.ac.be † Electronic address: a.s.alexandrov@lboro.ac.uk

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Section: Continuum Polaronmentioning

confidence: 99%

Fröhlich polaron and bipolaron: recent developments

2009

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“…The discontinuity between large and small polaron ground states can occur with the increase in the deformation potential interaction, not by the increase in the Fröhlich interaction [74][75][76]. The system in which small polarons are stabilized by the short-range interaction becomes insulating [77,78]. At intermediate electron-densities, large and small polarons coexist in the metallic state near the boundary between metallic and insulating regions [79].…”

Section: T-u-s-n Diagrammentioning

confidence: 99%

Electrons of alkali metals in regular nanospaces of zeolites

Nakano

Nozue

2017

Advances in Physics: X

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The s-electrons of alkali metals loaded into regular nanospaces (nanocages) of zeolite crystals display novel electronic properties, such as a ferrimagnetism, a ferromagnetism, an antiferromagnetism, an insulator-to-metal transition, etc., depending on the kind of alkali metals, their loading density, and the structure type of zeolite frameworks. These properties are entirely different from those in bulk alkali metals of freeelectrons. Alkali-metal clusters are stabilized in cages of zeolites, and new quantum states of s-electrons, such as 1s, 1p, and 1d states in the spherical quantum-well model, are formed. An electron correlation, a polaron effect, and an orbital degeneracy in the quantum states of s-electrons play critical roles in taking on the novel electronic properties. Electronic properties can be overviewed systematically by a coarse-grained model of localized s-electron states in cages based on the tightbinding approximation, followed by the t-U-S-n diagram of the correlated polaron system given by the so-called HolsteinHubbard Hamiltonian: an electron transfer energy through windows of cages (t), a Coulomb repulsion energy between two s-electrons in the same cage (U), a short-range electron-phonon interaction energy due to the cation displacements (S), and an average number of s-electrons per cage (n). Beyond the jellium background model of alkali-metal clusters, a huge spin-orbit interaction has been observed in the 1p degenerate orbitals of clusters, similarly to the Rashba mechanism. ARTICLE HISTORY

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“…[68,69] that the existence of a finitemomentum ground state implies symmetry breaking and, consequently, a phase transition corresponding to the "selflocalization" transition of Landau and Pekar [2]. Although we will discuss states of the Hamiltonian (13) with arbitrary total momentum p, it was established rigorously in Ref.…”

Section: A Lee-low-pines Transformationmentioning

confidence: 99%

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Shashi¹,

Grusdt²,

Abanin³

et al. 2014

Phys. Rev. A

108

182

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Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here, we consider impurities with two or more internal hyperfine states, and study their radio-frequency (rf) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate rf spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is noninteracting, by performing a nonperturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions, the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The rf signal contains a δ-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The rf spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct rf measurement, in which the impurity is initially in an interacting state, and the inverse rf measurement, in which the impurity is initially in a noninteracting state. In the latter case, in order to calculate the rf spectrum, we solve the problem of polaron formation: a mobile impurity is suddenly introduced in a BEC, and dynamically gets dressed by Bogoliubov phonons. Our solution is based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, which becomes exact when the impurity is localized. Moreover, we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states are interacting with the BEC.

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Analytical properties of polaron systems or: Do polaronic phase transitions exist or not?

Cited by 228 publications

References 204 publications

Fröhlich polaron and bipolaron: recent developments

Fröhlich polaron and bipolaron: recent developments

Electrons of alkali metals in regular nanospaces of zeolites

Radio-frequency spectroscopy of polarons in ultracold Bose gases

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