Effective action and density-functional theory

Polónyi, János; Sailer, K.

doi:10.1103/physrevb.66.155113

Cited by 51 publications

(98 citation statements)

References 46 publications

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“…For example, an interesting option can be found in [75]. In most cases the norm (5.27) applied to G supposedly is the natural choice: the propagator G is the key input in ∆S 2 , any iterative truncation scheme involves powers of G and hence the importance of its supremum is enhanced within each iteration step 8 .…”

Section: Optimisation Criterionmentioning

confidence: 99%

“…In theories with a complicated phase structure this might necessitate introducing a large number of vertices to the effective action in terms of the fundamental fields. A way to avoid such a drawback is to reparameterise the theory in terms of the relevant degrees of freedom [41,[72][73][74][75][76][78][79][80][81][82].…”

Section: Truncation Schemes and Optimisationmentioning

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: Optimisation Criterionmentioning

confidence: 99%

Section: Truncation Schemes and Optimisationmentioning

confidence: 99%

Aspects of the functional renormalisation group

2007

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“…Here, we restrict ourselves to the leading order of the gradient expansion, the local-potential approximation (LPA). In order to get more insight in the RG evolution of the blocked action, it may turn out to be useful in the future to replace the gradient expansion with some more appropriate approximation scheme, like the cluster expansion proposed in [33]. In LPA the ansatz for the blocked action can be written as…”

Section: Rg Flow Of Gsgmmentioning

confidence: 99%

Renormalization-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d>~3 dimensions

2004

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Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d ≥ 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d ≥ 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.PACS numbers: 11.10.Hi, 11.10.Kk I. INTRODUCTIONThe renormalization of a two-dimensional one-component scalar field theory with a periodic self-interaction, and the two-dimensional generalized sine-Gordon model (GSGM) have been investigated for d = 2 dimensions in great detail over the last three decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Here, we only mention some of the main results:• The blocked potential for the two-dimensional GSGM tends to a constant effective potential in the IR limit, independent of the field [12,13,14].• Following the procedure proposed in [16], one can identically rewrite the partition function of the d-dimensional GSGM in the form of a d-dimensional static Coulomb gas, which we call here the equivalent Coulomb gas (ECG). For d = 2 it is well-known that the GSGM and the ECG, as well as the XY model describing classical planar spins belong to the same universality class [10]. The XY model has a dual theory in the sense of [17] that can be reformulated as a gas of topological excitations: the two-dimensional vortex gas (VG) for d = 2, and the three-dimensional vortex-loop gas (VLG) for d = 3 (see [10] and Refs. therein). For dimensions d = 2, it was shown that the ECG and the VG can be transformed into one another by an appropriate duality transformation [3,7,8,15] that inverts the temperature. Two-dimensional generalized models are well known where both the ECG and the VG are included as particular limiting cases [3,7,8,15] and are self-dual under the duality transformation.While the relations of the various models for two dimensions are well-established, those of the corresponding models for d = 3 are not completely settled (see e.g. [10]). In particular, it is not proven that the VLG and the threedimensional XY-model belong to the same class of universality. Therefore, the investigation of the renormalization of the GSGM and the ECG for d ≥ 3 dimensions is essential for a further clarification of this issue. The purpose of the present work is threefold:1. to investigate the renormalization of the GSGM for dimensions d ≥ 2 by the Wegner-Houghton renormalizationgroup (WH-RG) method [18] and to demonstrate numerically tha...

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“…This means that the computational cost for DFT is far less than for wave function methods and the calculations can be applied to heavy nuclei. DFT is naturally formulated in an effective action framework [85] and carried out using an inversion method implemented with EFT power counting [86,87,88]. The simple prototype EFT from Section 2 for a dilute system can be revisited in DFT by putting the fermions in a trap potential v ext (x) (e.g., a harmonic oscillator) and adding sources coupled to external densities [89].…”

Section: Density Functional Theory As An Eftmentioning

confidence: 99%