Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars

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.

Fermi surfaces and gauge-gravity duality

“…The challenge for the future is to describe the phases of Sections V and VI using the dual gravity theory, in a manner which captures their expected properties of finite-range models in d = 2 and d = 3 respectively, and there have been recent studies in this direction [10,[12][13][14][15][16][17][18]20]. In particular, the d = 3 model of Gubser and Rocha [10] is a promising model for future study.…”

“…An analogy with the Fermi gas at unitarity helps clarify this point: this theory contains a composite boson which can be either canonical or non-canonical, and the choice only distinguishes different perturbative expansions of the same physics. [51,52] Also, with attractive gauge forces between the b± bosons and f ± fermions, we can expect that they form multiple bound states, and each of these lead to separate Fermi surfaces: in particular, this expected from the multiple Fermi surfaces seen in a recent holographic analysis [14,15]. For simplicity, we will only consider a single such bound state, and a single c fermion here, but it is not difficult to extend our analysis to multiple c fermions.…”

“…Just as in Eq. (3.3), we can decouple this interaction by introducing a color-singlet fermionic field c. As in Section V, there can be numerous such bound states of the gauge-charged bosons and fermions [14,15], but, for simplicity, we will only include a single gauge-invariant and canonical fermion. Our theory becomes…”

The Landscape of the Hubbard Model

“…(7.6). A number of recent theories [75][76][77][78][79][80][81][82][83][84] have examined the feedback of the finite density matter on the metric of the AdS space, and found that the AdS 2 horizon disappears at T = 0, and is replaced by a metric with a finite value of z. Many physical properties of such holographic metals are similar to those of the field theory in Eq.…”

A comment on holographic Luttinger theorem

“…In [9][10][11], it was pointed out that a holographic system with a charged bulk fermion, which is called "electron star" in the literature, exhibits the Luttinger theorem of the boundary fermion theory. This is based on the observation that the bulk fermions obey a bulk Luttinger theorem at each radius for the electron star.…”