Critical behavior of Tomonaga-Luttinger liquids with a mobile impurity

Tsukamoto, Yasumasa; Fujii, T.; Kawakami, Norio

doi:10.1103/physrevb.58.3633

Cited by 30 publications

(65 citation statements)

References 28 publications

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“…Previous work of a mobile impurity embedded into a Fermi gas should be pointed out [21][22][23][24][25][26][27][28][29][30]. Although these papers are closely related to the present work and Refs.…”

Section: Introductionmentioning

confidence: 78%

Threshold singularities in a Fermi gas with attractive potential in one dimension

Schlottmann

Zvyagin

2015

Nuclear Physics B

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We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ-function potential using the Bethe Ansatz solution. In zero magnetic field the atoms form bound states of N = 2S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c = 1. The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe Ansatz solution we obtain expressions for the critical exponents for the single-particle (hole) Green's function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.

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Section: Introductionmentioning

confidence: 78%

Threshold singularities in a Fermi gas with attractive potential in one dimension

Schlottmann

Zvyagin

2015

Nuclear Physics B

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“…[22][23][24][25] It was shown 23 that the spectrum of highenergy excitations with S z =0,1 contains an edge singularity with a nontrivial field dependence of the edge frequency which in the idealized model with no interaction except the hard-core constraint is given by 0 = ͑1−S z ͒H. The spectral function of a mobile impurity in the TL liquid has been extensively studied theoretically; 26,27 however, to our knowledge, no numerical results are available to compare with the theoretical predictions. An alternative bosonization description including high-energy modes has been proposed recently.…”

Section: Introductionmentioning

confidence: 99%

Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields

et al. 2007

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We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of an S = 1 Heisenberg chain, placed in a strong external magnetic field H exceeding the Haldane gap ⌬, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range տ⌬ the longitudinal ͑with respect to the applied field͒ dynamical structure factor is dominated by the power-law singularity S ʈ ͑q = , ͒ ϰ ͑ − 0 ͒ −␣Ј . We study the behavior of the high-energy edge exponent ␣Ј and the edge 0 as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at H Ͼ⌬ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.

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“…17 In the finite hole case shown in Fig. 4͑a͒ one can transform to a frame comoving with the excited hole ͑Castro Neto and Fisher, 1996;Tsukamoto, 1998a. In this frame the Hamiltonian takes the form H = H elec + H elec−hole + H hole , where…”

Section: B Fermi-edge Singularitymentioning

confidence: 99%

Colloquium: The spin-incoherent Luttinger liquid

2007

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In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that "low energy" describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.

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Critical behavior of Tomonaga-Luttinger liquids with a mobile impurity

Cited by 30 publications

References 28 publications

Threshold singularities in a Fermi gas with attractive potential in one dimension

Threshold singularities in a Fermi gas with attractive potential in one dimension

Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields

Colloquium: The spin-incoherent Luttinger liquid

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