Transverse Gauge Interactions and the Vanquished Fermi Liquid

Chakravarty, Sudip; Norton, Richard; Syljuåsen, Olav F.

doi:10.1103/physrevlett.74.1423

Cited by 113 publications

(119 citation statements)

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“…It is known that in this case the system shows non-Fermi-liquid behavior for Dр3, manifested in properties like the specific heat or anomalous electron field dimensions. [11][12][13] In the present work, we address the applicability of the notion of Fermi-liquid fixed point to two-dimensional systems with unscreened Coulomb interaction. The absence of screening requires the vanishing of the density of states at the Fermi level.…”

Section: ͓S0163-1829͑99͒50204-x͔mentioning

confidence: 99%

“…Such nontrivial scaling of the Fermi velocity in the infrared seems to be also present in systems with gauge interactions. 12,13 To summarize, semimetals described by the twodimensional Dirac equation, such as a graphite layer, show significant differences with respect to the properties of standard Fermi liquids with ͑screened͒ Coulomb interactions. In the present problem, the quasiparticle lifetime goes like ϳlog 2 ( )/ , while the enhancement of the Fermi velocity implies the vanishing of the effective coupling in the infrared.…”

Section: Rapid Communicationsmentioning

confidence: 99%

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Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction

1999

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A full, nonperturbative renormalization group analysis of interacting electrons in a graphite layer is performed, in order to investigate the deviations from Fermi-liquid theory that have been observed in the experimental measures of a linear quasiparticle decay rate in graphite. The electrons are coupled through Coulomb interactions, which remain unscreened due to the semimetallic character of the layer. We show that the model flows towards the noninteracting fixed point for the whole range of couplings, with logarithmic corrections which signal the marginal character of the interaction separating Fermi-liquid and non-Fermi-liquid regimes. ͓S0163-1829͑99͒50204-X͔During recent years there has been important progress in understanding the properties of quantum electron liquids in dimension DϽ3. One of the most fruitful approaches in this respect springs from the use of renormalization group ͑RG͒ methods, in which the different liquids are characterized by several fixed points controlling the low-energy properties. The Landau theory of the Fermi liquid in dimension DϾ1 can be taken as a paradigm of the success of this program. It has been shown that, at least in the continuum limit, a system with isotropic Fermi surface and regular interactions is capable of developing a fixed point in which the interaction remains stable in the infrared. 1 The question of whether different critical points may arise at dimension Dϭ2 is now a subject of debate. [2][3][4][5] From the perspective of the RG approach, one of the premises leading to the Fermi-liquid fixed point should be relaxed in order to flow to a different universality class. In the case of models proposed to understand the electronic properties of copperoxide superconductors, the high anisotropy of the Fermi surface 6 may play an important role in the anomalous behavior of the normal as well as of the superconducting state. 7 On the other hand, a possible source of non-Fermi-liquid behavior may arise in systems with singular interactions. 8 In the case of the Coulomb interaction screened by the Fermi sea, a solution by means of bosonization methods has shown that no departures from Fermi-liquid behavior arise at Dϭ2 and 3. 9 It has been also shown for the conventional screened interaction that only potentials as singular as V(q) ϳ1/͉q͉ 2DϪ2 can lead to a different electron liquid. 8,10 The system of electrons with gauge interactions is quite different in that respect. It is known that in this case the system shows non-Fermi-liquid behavior for Dр3, manifested in properties like the specific heat or anomalous electron field dimensions. [11][12][13] In the present work, we address the applicability of the notion of Fermi-liquid fixed point to two-dimensional systems with unscreened Coulomb interaction. The absence of screening requires the vanishing of the density of states at the Fermi level. Semimetals show this behavior, while retaining a gapless electronic spectrum. The existence of a well-defined continuum at low energies permits the existence of nontrivial sca...

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Section: ͓S0163-1829͑99͒50204-x͔mentioning

confidence: 99%

Section: Rapid Communicationsmentioning

confidence: 99%

Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction

1999

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“…A particular consequence of this is the appearance of an anomalous contribution to the low-temperature limit of entropy and specific heat proportional to αT ln T −1 [1,2,3], but it was argued that the effect would be probably too small for experimental detection.…”

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confidence: 99%

Anomalous specific heat in high-density QED and QCD

2004

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Long-range quasi-static gauge-boson interactions lead to anomalous (non-Fermiliquid) behavior of the specific heat in the low-temperature limit of an electron or quark gas with a leading T ln T −1 term. We obtain perturbative results beyond the leading log approximation and find that dynamical screening gives rise to a low-temperature series involving also anomalous fractional powers T (3+2n)/3 . We determine their coefficients in perturbation theory up to and including order T 7/3 and compare with exact numerical results obtained in the large-N f limit of QED and QCD. PACS numbers: 11.10.Wx, 12.38.Mh, 71.45.Gm, 11.15.Pg It has been established long ago [1] in the context of a nonrelativistic electron gas that the only weakly screened low-frequency transverse gauge-boson interactions lead to a qualitative deviation from Fermi liquid behavior. A particular consequence of this is the appearance of an anomalous contribution to the low-temperature limit of entropy and specific heat proportional to αT ln T −1 [1, 2, 3], but it was argued that the effect would be probably too small for experimental detection.More recently, it has been realized that analogous non-Fermi-liquid behavior in ultradegenerate QCD is of central importance to the magnitude of the gap in color superconductivity [4,5,6], and it has been pointed out [7] that the anomalous contributions to the low-temperature specific heat may be of interest in astrophysical systems such as neutron or protoneutron stars, if they involve a normal (non-superconducting) degenerate quark matter component.So far only the coefficient of the αT ln T −1 term in the specific heat has been determined (with Ref.[3] correcting the result of Ref.[1] by a factor of 4), but not the complete argument of the leading logarithm. While the existence of the T ln T −1 term implies that there is a temperature range where the entropy or the specific heat exceeds the ideal-gas value, without knowledge of the constants "under the log" it is impossible to give numerical values for the required temperatures.Furthermore, a quantitative understanding of these anomalous contributions is also of interest with regard to the recent progress made in high-order perturbative calculations of the pressure (free energy) of QCD at nonzero temperature and chemical potential [8], where it has been found that dimensional reduction techniques work remarkably well except for a narrow strip in the T -µ-plane around the T = 0 line.In the present Letter we report the results of a calculation of the low-temperature entropy and specific heat for ultradegenerate QED and QCD which goes beyond the leading log approximation. Besides completing the leading logarithm, we find that for T /µ ≪ g ≪ 1, where g is either the strong or the electromagnetic coupling constant, the higher terms of the low-temperature series involve also anomalous fractional powers T (3+2n)/3 , and we give their coefficients through order T 7/3 . Our starting point is an expression for the thermodynamic potential of QED and QCD

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“…This program was carried out, with interesting results, for the Landau damped boson coupled to a Fermi surface in Ref. 10. The adjoint large N theory described here may also be applicable in d = 2 + 1.…”

Section: Discussionmentioning

confidence: 99%

“…A commonly adopted view has been that the anomalous power laws present in non-Fermi liquids cannot be understood without a controlled theory of the deep infrared behavior of the boson-fermion theory [8][9][10][11][12][13] . However, at finite temperature or frequency scales, a metal in the vicinity of a quantum critical point exhibits crossovers, not transitions, from Fermi liquid to nonFermi liquid scaling behavior.…”

Section: Introductionmentioning

confidence: 99%

Quantum critical metals ind=3+1dimensions

et al. 2013

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We study the problem of disorder-free metals in the vicinity of a quantum critical point in d = 3+1 dimensions. We begin with perturbation theory in the 'Yukawa' coupling between the electrons and undamped bosons (order parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the 'marginal Fermi liquid' phenomenology 1 . We discuss a large N theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.

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Transverse Gauge Interactions and the Vanquished Fermi Liquid

Cited by 113 publications

References 20 publications

Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction

Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction

Anomalous specific heat in high-density QED and QCD

Quantum critical metals ind=3+1dimensions

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