Fermionic Renormalization Group Flows: Technique and Theory

Salmhofer, Manfred; Honerkamp, Carsten

doi:10.1143/ptp.105.1

Cited by 289 publications

(411 citation statements)

References 4 publications

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“…FRG flows in gravity are investigated [142][143][144][145][146][147]. All these formal advances have been successfully used within applications, see reviews [15][16][17][18][19][20][21][22][23].…”

Section: Flowsmentioning

confidence: 99%

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Aspects of the functional renormalisation group

2007

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We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being N PI quantities. We discuss optimisation and derive a functional optimisation criterion.Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.

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Section: Flowsmentioning

confidence: 99%

“…It is not meant as a review and for a more complete list of references we refer the reader to the reviews already cited above, [15][16][17][18][19][20][21][22][23]. We close the introduction with an overview over the work.…”

mentioning

confidence: 99%

Aspects of the functional renormalisation group

2007

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“…General aspects of the fRG can be found in [23], [24], and [25], while its application to inhomogeneous LLs is described in [8], [11] and [16]. By comparison to results for small systems obtained by density-matrix renormalization group and to exact results from bosonization and Bethe ansatz for the asymptotic behavior, it was shown that the fRG in the truncation scheme used here captures the relevant physics not only in the asymptotic low-energy regime but also on finite energy scales [11,16].…”

Section: The Functional Renormalization Groupmentioning

confidence: 99%

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Wächter

Meden

Schönhammer

2009

J. Phys.: Condens. Matter

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Abstract. We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (twodimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, we compute the temperature dependence of the linear conductance G of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a G(T ) which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise setup the wide temperature regime of power-law scaling found in the end-coupled case is broken up in up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental setups designed for a verification of Luttinger liquid power-law scaling.

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“…The other strategy, which was pioneered by Morris [3] and has been preferentially used in the condensed matter community to study non-relativistic fermions [9,10], is based on the expansion of Γ in powers of the fields, leading to an infinite hierarchy of coupled integro-differential equations for the one-particle irreducible vertices. This approach has the advantage of providing information on the momentum-and frequency dependence of the vertices.…”

Section: Introductionmentioning

confidence: 99%

Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

Sinner¹,

Hasselmann²,

Kopietz³

2008

J. Phys.: Condens. Matter

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Abstract. We include spontaneous symmetry breaking into the functional renormalization group equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each renormalization group (RG) step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Σ(k) and interpolates between lowest order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Σ(k) = k 2 c σ − (|k|ξ, |k|/k c ), where ξ is the order parameter correlation length, k c is the Ginzburg scale, and σ − (x, y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we explicitly calculate within our truncation.

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Fermionic Renormalization Group Flows: Technique and Theory

Cited by 289 publications

References 4 publications

Aspects of the functional renormalisation group

Aspects of the functional renormalisation group

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

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