Non-Fermi-liquid behavior in quantum critical systems

Gan, Junwu; Wong, Eugene

doi:10.1103/physrevlett.71.4226

Cited by 82 publications

(118 citation statements)

References 24 publications

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“…This is in agreement with previous work [7,8,11], and points to a possible non-Fermi behavior in d ≤ 3, as previously observed in the context of gauge theories [11] and recently noted in the context of a ferromagnet [12]. To summarize, we introduced an RG scheme in the spirit of the Shankar approach [9], which allows to treat the fermion and the boson degrees of freedom in the spinfermion models on an equal footing.…”

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confidence: 73%

Scaling approach to itinerant quantum critical points

2004

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Based on phase space arguments, we develop a simple approach to metallic quantum critical points, designed to study the problem without integrating the fermions out of the partition function. The method is applied to the spin-fermion model of a T=0 ferromagnetic transition. Stability criteria for the conduction and the spin fluids are derived by scaling at the tree level. We conclude that anomalous exponents may be generated for the fermion self-energy and the spin-spin correlation functions below d = 3, in spite of the spin fluid being above its upper critical dimension. 78.20.Ls, 47.25.Gz, 76.50+b, 72.15.Gd One of the explanations advanced for the breakdown of the Fermi liquid theory in the normal state of high temperature superconductors is the proximity to a quantum critical point (QCP), hidden under the superconducting dome. The nature of this zero temperature transition remains controversial. However, in several heavy fermion materials, the Fermi liquid state was experimentally shown to break down near a well characterized T = 0 antiferromagnetic instability [1][2][3][4]. A detailed renormalization group study of QCPs in itinerant magnets was first undertaken by Hertz [5], and later augmented by Millis [6]. The key observation [5] was that spin fluctuations relax critically in time, with a dynamic exponent z relating the time and the length scales as τ ∼ ξ z . Thus a d-dimensional system can be viewed as having effective dimensionality d + z. For an antiferromagnetic QCP, one finds z = 2, while for a ferromagnetic QCP, z = 3. After integrating the fermions out of the partition function, the authors of [5,6] argued that, in d = 2 or 3 (the cases of interest for heavy fermions as well as high-T c superconductors), d + z ≥ 4. Thus the effective Ginzburg-Landau theory for the spin fluid falls above its upper critical dimension, and has Gaussian critical behaviour.Recently, the validity of integrating out the fermions has been questioned [7,8], since gapless fermions may lead to singular coefficients in the Ginzburg-Landau expansion. Another outstanding question is whether the Fermi liquid theory may break down in two or three dimensions, i.e. whether the quasiparticles may become illdefined while the magnetic fluctuations are only innocuously critical, being described by a Gaussian theory. In this case, the conduction and the magnetic fluids would behave as if decoupled, each having its own upper critical dimension. Finally, integrating out the fermions to describe a QCP in a metal is conceptually unsatisfactory, as it greatly complicates a consistent account of electron transport.In this paper, we introdice a simple scaling approach, designed to study a spin-fermion model at a QCP without integrating the fermions out of the partition function. Already at the tree level, it reveals that the critical behavior is controlled by several couplings, rather than by the single fermion-boson coupling constant g, expected naively. At a ferromagnetic quantum critical point, the coupling g becomes relevant below one sp...

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confidence: 73%

Scaling approach to itinerant quantum critical points

2004

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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%

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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“…There have been several studies of the two-particle correlation functions which concentrated on the non-renormalization of the gauge field propagator [11][12][13][14]16]. Recently three of us with Furusaki have examined several gauge invariant two-particle correlation functions for all ratios of ω and q [17].…”

Section: Introductionmentioning

confidence: 99%

“…They found that the gauge field fluctuations give rise to a singular contribution to the self-energy in the oneparticle Green's function of the composite fermions [5,8]. Later various kinds of methods were used to go beyond the perturbation theory [9][10][11][12][13][14][15][16], which were motivated by the fact that the singular self-energy correction leads to a divergent effective mass of the composite fermions [5]. If one applied this divergent effective mass to the Shubnikov-de Haas effect near ν = 1/2, one would find that the gap ∆ p of ν = p/(2p ± 1) FQH state goes down faster than 1/p as p → ∞:…”

Section: Introductionmentioning

confidence: 99%