Renormalization group flow for fermionic superfluids at zero temperature

Strack, Philipp; Gersch, R.; Metzner, Walter

doi:10.1103/physrevb.78.014522

Cited by 55 publications

(82 citation statements)

References 36 publications

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“…Similar parametrizations of the fermionic selfenergy have been studied in Gubbels & Stoof [24], Bartosch et al [25] and Strack et al [48]. Further, we include an atom-dimer interaction term.…”

Section: Running Fermion Sectormentioning

confidence: 99%

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Scherer

Floerchinger

Gies

2011

Phil. Trans. R. Soc. A.

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We review the functional renormalization group (RG) approach to the Bardeen-CooperSchrieffer to Bose-Einstein condensation (BCS-BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

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Section: Running Fermion Sectormentioning

confidence: 99%

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Scherer

Floerchinger

Gies

2011

Phil. Trans. R. Soc. A.

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“…To distinguish between longitudinal and transverse fluctuations, one may fix the phase of the order parameter α Λ such that α Λ is real, decompose the complex order parameter field in real and imaginary parts φ(q) = σ(q) + iπ(q) with σ(−q) = σ * (q) and π(−q) = π * (q), and introduce different renormalization factors for σ and π fields (Pistolesi et al, 2004). Using this decomposition, the correct infrared behavior was obtained by Strack et al (2008) where, however, the cancellation of singular contributions to the renormalization factors for the transverse π fields was implemented by hand. To capture this cancellation intrinsically, one has to include an additional U (1) symmetric gradient term of the form [σ(∂ x0 …”

Section: B Flows With Hubbard-stratonovich Fieldsmentioning

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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“…[25]. In contrast to a previous FRG calculation [21], we use here a scheme where the cutoff is introduced only in the bosonic part of the Gaussian propagator. The advantage of our boson cutoff scheme is that the initial condition for the fermionic self-energy is simply given by the self-consistent Hartree-Fock approximation (i.e.…”

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confidence: 99%

“…The unitary point has also been studied theoretically using Monte Carlo simulations [11,12] and various analytical methods based on field theoretical techniques [13,14,15,16,17] or the functional renormalization group (FRG) [18,19,20,21], but also in this case the theoretical results have not converged yet. In such a situation it is desirable to study this problem using new approximation strategies which are complementary to previous calculations.…”

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confidence: 99%

Renormalization of the BCS-BEC crossover by order-parameter fluctuations

2009

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We use the functional renormalization group approach with partial bosonization in the particleparticle channel to study the effect of order parameter fluctuations on the BCS-BEC crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid order parameter at the unitary point and compare our results with experiments and previous calculations.PACS numbers: 03.75.Ss, 03.75.Hh, 74.20.Fg The BCS-BEC crossover in a two-component Fermi gas has attracted the attention of theorists for several decades [1,2,3,4,5]. It is generally accepted that the nature of the superfluid state exhibits a smooth crossover as a function of the dimensionless parameter 1/k F a s , where k F is the Fermi momentum and a s is the s-wave scattering length in vacuum. While for a small negative scattering length, i.e., 1/k F a s ≪ −1, the paired state generated by the attractive interaction is a collection of spatially extended Cooper pairs (BCS limit), in the opposite limit 1/k F a s ≫ 1 the superfluid state can be viewed as a Bose-Einstein condensate of tightly bound fermion pairs (BEC limit). Of particular interest is the unitary point 1/k F a s = 0 where the scattering length diverges and k F sets the only length scale of the system. In this regime quantitative calculations are difficult because there is no small parameter to justify approximations.In the past few years several observables such as the chemical potential and the quasi-particle gap have been determined experimentally at the unitary point [6,7,8,9,10], but there is still some uncertainty in the precise numerical values of these quantities. The unitary point has also been studied theoretically using Monte Carlo simulations [11,12] and various analytical methods based on field theoretical techniques [13,14,15,16,17] or the functional renormalization group (FRG) [18,19,20,21], but also in this case the theoretical results have not converged yet. In such a situation it is desirable to study this problem using new approximation strategies which are complementary to previous calculations. In this work we shall therefore develop a novel FRG approach for the BCS-BEC crossover which is based on a suitable truncation of the vertex expansion using skeleton equations and Ward identities. For fixed density we explicitly calculate the chemical potential, the single-particle gap, and the superfluid order-parameter at the unitary point in three dimensions, and compare our results with experiments and with previous calculations.We consider a system of neutral fermions with energy dispersion ǫ k = k 2 /(2m) and a short-range attractive two-body interaction g p depending on the total momentum p of a fermion pair. After decoupling the intera...

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Renormalization group flow for fermionic superfluids at zero temperature

Cited by 55 publications

References 36 publications

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Functional renormalization group approach to correlated fermion systems

Renormalization of the BCS-BEC crossover by order-parameter fluctuations

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