Table of Links Prologue
Diagrammatic(s) Rules
Straight-forward Eikonal
Legacy Bosonization
Wonton Holography
Holographic Propagators
Strange Cuprates
Stranger Things
Epilogue Prologue Prologue Diagrammatic(s) Rules Diagrammatic(s) Rules Straight-forward Eikonal Straight-forward Eikonal Legacy Bosonization Legacy Bosonization Wonton Holography Wonton Holography Holographic Propagators Holographic Propagators Strange Cuprates Strange Cuprates Stranger Things Stranger Things Epilogue Epilogue Stranger Things The propagator (21) obtained with the use of (44) was shown to develop three distinct FS [44], thus hinting at flattening of the renormalized fermion dispersion and bringing about an intrinsic instability towards the formation of a ’flat band’ characterized by z > 1 [20, 45]. Interestingly, if the interaction function D(ω, k) were to be molded into (1) by choosing ρ = 2 and ξ → −∞ the HV exponents would be taking values z = 1, θ = 0, thus satisfying (41) but not (40). On the other hand, matching the holographic asymptotics (31) would only be possible for θ = 2 which doesn’t satisfy (40) either. The interactions (1) with ξ = ρ = 1 also arise in the 2d problem of half-filled Landau level with unscreened Coulomb interactions [5]. The first-order self-energy (4) now demonstrates a ’marginal FL’ behavior In the N → 0 limit one then obtains the counterpart of (11) which would be marginally consistent - as far as the overall power-counting is concerned - with the holographic action (31) that would yield mere constants (or, at most, logarithms) for z = 1 and θ = 0 in both large-r and -τ limits. Similar to the discussion of the case ξ = 1, it has been argued that the behavior (46) can only develop in some intermediate regime. By contrast, at the longest times an essentially free algebraic behavior, G(τ, r → 0) ≈ G0(τ, r → 0), was found, whereas at large distances the propagator was predicted to experience no more than a logarithmic suppression, G(τ → 0, r) ≈ G0(τ → 0, r)/ ln r [8]. Yet another physically relevant example of the 2d interaction (1) with ρ = 2, ξ = 0 corresponds to the socalled ’spin-fermion’ model of itinerant fermions coupled by antiferromagnetic fluctuations where the momentum k is measured with respect to the AFM ordering vector [46]. Neglecting the (in fact, all-important) complications associated with a non-circular shape of the realistic FS one computes (10) in the form Also, the theory of compressible even-denominator QHE states that were originally described in terms of the finite density ’composite fermions’ [5], was later reformulated to elucidate its hidden Dirac properties [47, 48]. In 1d the pseudo-relativistic behavior sets in generically in the presence of partially filled bands. By using the standard bosonization one readily obtains the faster-than-algebraic decay of the propagator [49] that can be thought of as the 1d analog of the Mott insulating state. Considering that in 1d no Landau damping can occur, the formal values of the HV exponents, z = 1 and θ = 0, obtained from (4) and (41) for ρ = 0 and ξ → −∞ yield the asymptotics (31) whose power counting is roughly consistent with (48). Contrary to the original expectations, though, the amplitude (49) was shown to manifest η3 < 0 under the use of a gauge invariance-preserving regularization scheme [51]. Obviously, being just one (albeit a rather natural one) out of infinitely many other gauge-invariant amplitudes the function (49) may not be necessarily representative of the general behavior. In fact, its dependence on the contour Γ is somewhat reminiscent of that on the gauge in the case of the ordinary (non-gauge-invariant, albeit unique) propagator. Author:
(1) D. V. Khveshchenko, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599. Author: Author: (1) D. V. Khveshchenko, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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