Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions

Pirooznia, Peyman; Schütz, Florian; Kopietz, Peter

doi:10.1103/physrevb.78.075111

Cited by 12 publications

(13 citation statements)

References 40 publications

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“…Evaluating the intergrals and extracting the leading divergence requires steps similar to the ones taken to compute the first order RPA-like diagram χ b 1 (q, ω) of Eq. (16). The leading behavior close to the lower threshold is…”

Section: Second Order Perturbation Theorymentioning

confidence: 94%

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Investigating the roots of the nonlinear Luttinger liquid phenomenology

2019

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The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the twoparticle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.

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Section: Second Order Perturbation Theorymentioning

confidence: 94%

“…The idea is to include these perturbatively in the computation of observables and correlation functions [3]. However, the attempts in this direction led to divergences which indicate a breakdown of the corresponding perturbation theory [13][14][15][16]. The insights gained along this route are thus rather limited.…”

Section: Introductionmentioning

confidence: 99%

Investigating the roots of the nonlinear Luttinger liquid phenomenology

2019

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“…For our model, the three-loops can be calculated analytically using the method outlined in the appendix of Ref. 48. Consider first the non-symmetrized three-loop defined in Eq.…”

Section: Appendix B: the Symmetrized Three-loopmentioning

confidence: 99%

“…In particular, the initial condition for the vertex with three external boson legs is For our model, the three-loops can be calculated analytically using the method outlined in the appendix of Ref. 48. Consider first the non-symmetrized three-loop defined in Eq.…”

Section: Appendix B: the Symmetrized Three-loopmentioning

confidence: 99%

Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals

et al. 2012

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Using functional renormalization group methods, we study an effective low-energy model describing the Ising-nematic quantum critical point in two-dimensional metals. We treat both gapless fermionic and bosonic degrees of freedom on equal footing and explicitly calculate the momentum and frequency dependent effective interaction between the fermions mediated by the bosonic fluctuations. Following earlier work by S.-S. Lee for a one-patch model, Metlitski and Sachdev [Phys. Rev. B 82, 075127] recently found within a field-theoretical approach that certain three-loop diagrams strongly modify the one-loop results, and that the conventional 1/N expansion breaks down in this problem. We show that the singular three-loop diagrams considered by Metlitski and Sachdev are included in a rather simple truncation of the functional renormalization group flow equations for this model involving only irreducible vertices with two and three external legs. Our approximate solution of these flow equations explicitly yields the vertex corrections of this problem and allows us to calculate the anomalous dimension η ψ of the fermion field.

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“…and its modifications have been investigated actively [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. These studies have demonstrated that combined effect of the marginal and the irrelevant operators has important and measurable consequences for system's properties.…”

mentioning

confidence: 99%

One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior

Rozhkov

2014

Phys. Rev. Lett.

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It is well-known that, generically, the one-dimensional interacting fermions cannot be described in terms of the Fermi liquid. Instead, they present different phenomenology, that of the TomonagaLuttinger liquid: the Landau quasiparticles are ill-defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine-tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both the Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both the Tomonaga-Luttinger liquid and the Fermi liquid. Similar to the Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates finite discontinuity at the Fermi energy, which is a hallmark feature of the Fermi liquid. Possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.Introduction.-An important goal of the modern manybody physics is the search for exotic states of matter. Appropriate examples are spin liquids [1][2][3], Majorana fermion [4][5][6][7][8], topological insulators and semimetals [9][10][11], and others. A peculiar state of one-dimensional (1D) fermionic matter deviating from known types of interacting Fermi systems is the subject of this paper.Let us remind ourselves that the most basic model of the interacting fermions is that of the Fermi liquid. It successfully describes a variety of interacting fermion systems (e. g., electrons in solids, atoms of helium-3) [12]. The approach is based on the Landau's conjecture that both the ground state of a Fermi liquid and its low-lying excitations are adiabatically connected to states of the non-interacting Fermi gas. If the interaction is weak, this hypothesis implies that the perturbation theory in the interaction strength is valid. The latter supplies a theorist with a tool to study specific examples.A known system for which the Landau conjecture fails is a 1D liquid of interacting fermions. The interacting 1D fermions constitute a separate universality class, so-called Tomonaga-Luttinger liquid [13,14]: unlike the Fermi liquid, the Tomonaga-Luttinger ground and excited states have zero overlap with the corresponding non-interacting states, the Tomonaga-Luttinger liquid properties cannot be calculated perturbatively with interaction strength as a small parameter.In 1D the Tomonaga-Luttinger liquid is a generic state of matter. However, recent progress in fabrication and control over the properties of the many-particle systems allows us to look for more fragile types of 1D correlated liquids. Specifically, consider a gas of Fermi atoms in a 1D trap [15]. It is within modern experimental capabilities to vary the effective interaction constant of the opt...

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Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions

Cited by 12 publications

References 40 publications

Investigating the roots of the nonlinear Luttinger liquid phenomenology

Investigating the roots of the nonlinear Luttinger liquid phenomenology

Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals

One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior

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