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Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars
High Energy Physics - Theory · Submitted 10 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It follows that our system is a non-Fermi liquid that nonetheless exhibits Kosevich-Lifshitz quantum oscillations.
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The abstract, sentence by sentence
We apply a small magnetic field to strongly interacting matter with a gravity dual description as an electron star. These systems are both metallic and quantum critical at low energies. The resulting quantum oscillations are shown to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. It is seen that only fermions at a single radius in the electron star contribute to the oscillations. We proceed to show that the Fermi surface area extracted from the quantum oscillations does not obey the simplest statement of the Luttinger theorem, that is, it is not universally proportional to the total charge density. It follows that our system is a non-Fermi liquid that nonetheless exhibits Kosevich-Lifshitz quantum oscillations. We explain how the Luttinger count is recovered via a field theoretic description involving a continuum of `smeared' fermionic excitations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We apply a small magnetic field to strongly interacting matter with a gravity dual description as an electron star. | method 0.64 | 0.90 | 0.03 | asserted 0.92 |
| s1 | These systems are both metallic and quantum critical at low energies. | background 0.91 | 0.18 | 0.04 | asserted 1.00 |
| s2 | The resulting quantum oscillations are shown to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. | result 0.99 | 0.84 | 0.10 | asserted 1.00 |
| s3 | It is seen that only fermions at a single radius in the electron star contribute to the oscillations. | result 1.00 | 0.88 | 0.08 | asserted 1.00 |
| s4 | We proceed to show that the Fermi surface area extracted from the quantum oscillations does not obey the simplest statement of the Luttinger theorem, that is, it is not universally proportional to the total charge density. | result 0.99 | 0.93 | 0.53 | asserted 1.00 |
| s5 | It follows that our system is a non-Fermi liquid that nonetheless exhibits Kosevich-Lifshitz quantum oscillations. | interpretation 0.90 | 0.86 | 0.55 | asserted 1.00 |
| s6 | We explain how the Luttinger count is recovered via a field theoretic description involving a continuum of `smeared' fermionic excitations. | interpretation 0.71 | 0.87 | 0.21 | asserted 1.00 |
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The paper
Original abstract
We apply a small magnetic field to strongly interacting matter with a gravity dual description as an electron star. These systems are both metallic and quantum critical at low energies. The resulting quantum oscillations are shown to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. It is seen that only fermions at a single radius in the electron star contribute to the oscillations. We proceed to show that the Fermi surface area extracted from the quantum oscillations does not obey the simplest statement of the Luttinger theorem, that is, it is not universally proportional to the total charge density. It follows that our system is a non-Fermi liquid that nonetheless exhibits Kosevich-Lifshitz quantum oscillations. We explain how the Luttinger count is recovered via a field theoretic description involving a continuum of `smeared' fermionic excitations.
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References
How the literature uses it
38 arXiv papers cite this in 86 sentences
Papers citing it · 57 sentences without a confident label
Contests it 1 paper
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This conclusion is not intrinsic to holographic states supported by fermions, but rather is an artifact of the Thomas-Fermi approximation used in the pioneering work on electron stars [ref] .
A quantum electron star · Introduction · contest 0.77
Builds on it 1 paper
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As said in [ref] the arguments used to demonstrate this feature could be generalized to higher dimensions, showing that even in AdS$_5$ Kosevich-Lifshitz oscillations are present, nevertheless the Luttinger theorem is violated.
A Study on Charged Neutron Star in $AdS_5$ · Kosevich-Lifshitz oscillations in $AdS_5$ neutron star · 0.81
Uses its method or tool 2 papers
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We will present a fully self-consistent computation, including the back-reaction of the mesinos on the metric, using the approximation of the `electron star' theories [ref] .
Hidden Fermi surfaces in compressible states of gauge-gravity duality · Violation of hyperscaling, entropy, and entanglement entropy · 0.86
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One can treat the fermions as an ideal fluid and use a fermionic equation of state as Hartnoll and his collaborators did in their electron star papers [ref] .].
Crystalline geometries from fermionic vortex lattice with hyperscaling violation · Background Setup · 0.89
Compares with it 5 papers
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This is analogous to the smearing described in [ref] .
Friedel Oscillations in Holographic Metals · Lack of Friedel Oscillations · 0.96
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It also differs from earlier holographic results obtained in a probe limit in [ref] and appears to be due to the gravitational back-reaction which is included in our model.
Magnetic oscillations in a holographic liquid · Introduction · 0.98
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[ref] works in the “electron star” geometry [ref] which is also characterized by an IR Lifshitz geometry, but with $z ∼O(1)$, for which there is not an intermediate AdS$_2$ region.
Semi-local quantum liquids · Discussion · 0.98
Cites it as support 1 paper
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This is consistent with a boundary theory comprised of a continuum of Fermi surfaces, as proposed in [ref] .
Friedel Oscillations in Holographic Metals · Discussion · 0.97
Cites it as background 17 papers
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Some progress has been made recently in using holography to learn about metallic states of matter which are not described by Landau's Fermi liquid theory [ref] .
A quantum electron star · Introduction · 0.99
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Much recent work [ref] has described the compressible, non-superfluid states of quantum matter by the methods of gauge-gravity duality.
A model of a Fermi liquid using gauge-gravity duality · Introduction · 0.98
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Recent work has argued that `electron stars', a planar fluid of charged fermions in Anti-de Sitter space in equilibrium under gravitational and electromagnetic forces, provide a compelling holographic framework in which to study metallic quantum criticality [ref] .
Electron star birth: A continuous phase transition at nonzero density · Introduction · 0.87
What it cites · 28 sentences without a confident label
Uses the method or tool of 2 papers
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While performing the sums in ([ref]) is a standard computation, we will outline the method used in [ref] which extracts the oscillating part efficiently and transparently.
Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence · Magnetic field probe of electron stars · 1.00
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In the dual bulk description this amounts to solving the Einstein-Maxwell-fluid equations as was done in [ref] .
Electron stars for holographic metallic criticality · Field theory: Smeared Fermi surface and Landau bands · 0.97
Compares with 2 papers
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Without backreaction, the entire charge is carried by the black hole and the multiple probe Fermi surfaces include cases for which the quantum oscillations are not Kosevich-Lifshitz [ref] .
Quantum oscillations and black hole ringing · Magnetic field probe of electron stars · 0.89
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Without backreaction, the entire charge is carried by the black hole and the multiple probe Fermi surfaces include cases for which the quantum oscillations are not Kosevich-Lifshitz [ref] .
Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence · Magnetic field probe of electron stars · 0.89
Cites as background 2 papers
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A self gravitating fluid of charged fermions in asymptotically Anti-de Sitter space was termed an `electron star' in [ref] by analogy with the familiar neutron stars of astrophysics [ref] , which satisfy very similar equations.
Electron stars for holographic metallic criticality · Introduction · 0.84
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In these cases we can place the theory at a nonzero chemical potential $μ$ for a global $U(1)$ symmetry and flow to energy scales $E ≪μ$ [ref] .
Lectures on holographic methods for condensed matter physics · Introduction · 0.96
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