Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

Ledowski, Sascha; Kopietz, Peter; Ferraz, A.

doi:10.1103/physrevb.71.235106

Cited by 15 publications

(25 citation statements)

References 28 publications

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“…10,14,[16][17][18][19][20][21][22][23][24][25][26][27][28][29] However, the problem of self-consistently calculating the true Fermi surface has only recently been addressed. 10,14,25 At low energies all possible scattering processes in the spinless two-chain system can be divided into four different classes. 16 ͑1͒ Forward scattering processes, parametrized in terms of three different coupling constants f ++ , f −− , and f +− = f −+ , where the labels indicate the band of the fermions involved in the scattering process.…”

Section: Effective Low-energy Modelmentioning

confidence: 99%

“…14 We therefore propose an alternative truncation scheme based on the truncation according to relevance in the RG sense. In our model we have to keep track of the RG flow of the two relevant couplings r l , = ± 1, and the marginal couplings Z l , ṽ l , and ␥ l .…”

Section: A Truncation Based On Relevancementioning

confidence: 99%

“…It turns out that with this approach we can analyze the regime where the dimensionless interchain backscattering interaction g 0 is of the order of unity. The crucial point is that from the weak coupling analysis 14 we know that the confinement transition is driven by interchain backscattering, so that it is natural to decouple the interaction in this scattering channel via a suitable bosonic Hubbard-Stratonovich field. Simple truncations in the resulting mixed boson-fermion theory correspond to infinite resummations in an expansion of the RG ␤ functions in powers of g 0 .…”

Section: Introductionmentioning

confidence: 99%

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Fermi-surface renormalization and confinement in two coupled metallic chains

Ledowski

Kopietz

2007

Phys. Rev. B

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Using a nonperturbative functional renormalization group approach involving both fermionic and bosonic fields we calculate the interaction-induced change of the Fermi surface of spinless fermions moving on two chains connected by weak interchain hopping t Ќ . For a model containing interband backward scattering only we show that the distance ⌬ between the Fermi momenta associated with the bonding and the antibonding band can be strongly reduced, corresponding to a large reduction of the effective interchain hopping t Ќ * ϰ⌬. A self-consistent one-loop approximation neglecting marginal vertex corrections and wave-function renormalizations predicts a confinement transition for sufficiently large interchain backscattering, where the renormalized t Ќ * vanishes. However, a more accurate calculation taking vertex corrections and wave-function renormalizations into account predicts only weak confinement in the sense that 0 Ͻ ͉t Ќ * ͉ Ӷ ͉t Ќ ͉. Our method can be applied to other strong-coupling problems where the dominant scattering channel is known.

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Section: Effective Low-energy Modelmentioning

confidence: 99%

Section: A Truncation Based On Relevancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fermi-surface renormalization and confinement in two coupled metallic chains

Ledowski

Kopietz

2007

Phys. Rev. B

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“…For quasi-1D models with a small transverse hopping in a second direction the change from a gapless Luttinger liquid in a strictly one-dimensional situation to Fermi liquid instabilities toward ordering can be monitored as a function of the transverse hopping (Honerkamp and Salmhofer, 2003). The Fermi surface in coupled metallic chains was studied by Ledowski and Kopietz (2007a,b); Ledowski et al (2005). The possibility of triplet pairing driven by density wave fluctuations has been explored in such situations (Nickel et al, 2005(Nickel et al, , 2006.…”

Section: Other Systemsmentioning

confidence: 99%

Functional renormalization group approach to correlated fermion systems

et al. 2012

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Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems, (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals, (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and non-equilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. We present a self-contained derivation of the exact flow equations and describe frequently used truncation schemes. Reviewing selected applications we then show how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.

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“…This calculation is more complicated than in the case of two Fermi points, because a self-consistent treatment within renormalized perturbation theory requires the introduction of four counterterms, one for each Fermi point 14,15 . Vollhardt et al 21 pointed out that a large asymmetry in the DOS with a peak at the lower band edge tends to favor ferromagnetism by minimizing the increase of kinetic energy due to the spin polarization.…”

Section: Discussionmentioning

confidence: 99%