An exact integral equation for the renormalized Fermi surface

Ledowski, Sascha; Kopietz, Peter

doi:10.1088/0953-8984/15/27/309

Cited by 17 publications

(25 citation statements)

References 25 publications

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“…of the two-point vertex (2) flows into a RG fixed point 15 . Defining the rescaled four-point vertex viã…”

Section: Exact Rg Equation For the Fermi Surfacementioning

confidence: 99%

“…In this work we shall use our general method 12,13,14,15 of obtaining the FS as a RG fixed point to derive the self-consistency conditions for the true Fermi momenta k a F and k b F of two coupled spinless chains. In the parameter regime where the coupled chain system is a stable Luttinger liquid, these conditions can be cast into a simple transcendental equation for the distance ∆ = k b F −k a F between the Fermi momenta, which for small t ⊥ and for weak interactions takes the form…”

Section: Introductionmentioning

confidence: 99%

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Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

2005

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“…of the two-point vertex (2) flows into a RG fixed point 15 . Defining the rescaled four-point vertex viã…”

Section: Exact Rg Equation For the Fermi Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

2005

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“…As shown in Refs. 20,22, and 31, the renormalized Fermi surface can be defined as a fixed point of the RG and can in principle be calculated self-consistently entirely within the RG framework.…”

Section: Introductionmentioning

confidence: 99%

“…36 The latter are rather difficult to describe within the purely fermionic parametrizations used in Refs. 15,16,17,18,19,20,21,22,23,24,25,26,27. Naturally, a formulation of the functional RG where both fermionic and bosonic excitations are treated on equal footing should lead to a more convenient parametrization.…”

Section: Introductionmentioning

confidence: 99%

Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model

2005

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We develop a new formulation of the functional renormalization group (RG) for interacting fermions. Our approach unifies the purely fermionic formulation based on the Grassmannian functional integral, which has been used in recent years by many authors, with the traditional Wilsonian RG approach to quantum systems pioneered by Hertz [Phys. Rev. B 14, 1165], which attempts to describe the infrared behavior of the system in terms of an effective bosonic theory associated with the soft modes of the underlying fermionic problem. In our approach, we decouple the interaction by means of a suitable Hubbard-Stratonovich transformation (following the Hertzapproach), but do not eliminate the fermions; instead, we derive an exact hierarchy of RG flow equations for the irreducible vertices of the resulting coupled field theory involving both fermionic and bosonic fields. The freedom of choosing a momentum transfer cutoff for the bosonic soft modes in addition to the usual band cutoff for the fermions opens the possibility of new RG schemes. In particular, we show how the exact solution of the Tomonaga-Luttinger model (i.e., one-dimensional fermions with linear energy dispersion and interactions involving only small momentum transfers) emerges from the functional RG if one works with a momentum transfer cutoff. Then the Ward identities associated with the local particle conservation at each Fermi point are valid at every stage of the RG flow and provide a solution of an infinite hierarchy of flow equations for the irreducible vertices. The RG flow equation for the irreducible single-particle self-energy can then be closed and can be reduced to a linear integro-differential equation, the solution of which yields the result familiar from bosonization. We suggest new truncation schemes of the exact hierarchy of flow equations, which might be useful even outside the weak coupling regime.

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“…However, the knowledge of the exact shape of the FS of a material is very important since it may affect the transport properties as well as the collective behavior, and have valuable information from the point of view of theory in order to find the appropriate model to study the system. Many approaches have been used to study this problem such as mean field, 12,13 pertubation theory, 14 bosonization methods, 15,16 or perturbative renormalization group calculations, [17][18][19][20][21] and the cellular dynamical mean-field theory ͑CDMFT͒, an extension of dynamical mean field theory, 22 and many others. Despite great theoretical effort done in the last years, there is a need to develop alternative new methods in order to understand the origin of the electronic properties in materials with strong correlations.…”

Section: Introductionmentioning

confidence: 99%

Self-energy corrections to anisotropic Fermi surfaces

et al. 2006

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The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper-oxide superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is nontrivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.

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An exact integral equation for the renormalized Fermi surface

Cited by 17 publications

References 25 publications

Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model

Self-energy corrections to anisotropic Fermi surfaces

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