Bekenstein-Hawking Entropy and Strange Metals

By S. Sachdev. 2015

562 citations recorded by the source corpus.

We examine models of fermions with infinite-range interactions which realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$, and a non-zero entropy density $\mathcal{S}$ at vanishing temperature. Real time correlators of operators carrying U(1) charge $q$ at a low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency $\omega_{\mathcal{S}} = (q \, T/\hbar) (\partial \mathcal{S}/\partial{\mathcal{Q}})$ which determines a spectral asymmetry. We show that the correlators match precisely with those of the AdS$_2$ horizons of extremal charged black holes. On the black hole side, the matching employs $\mathcal{S}$ as the Bekenstein-Hawking entropy density, and the laws of black hole thermodynamics which relate $(\partial{\mathcal{S}}/\partial{\mathcal{Q}})/(2 \pi)$ to the electric field strength in AdS$_2$. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/13a6fae70fcec66bbf1f64a73c8349692eb8c4f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Stanford
2. J. Maldacena
3. S. Shenker
4. Alexei Y. Kitaev
5. V. Rosenhaus
6. Phil Saad
7. G. Turiaci
8. D. Harlow

In Atomic and Molecular Physics, and Optics

1. D. Stanford
2. Phil Saad
3. Alexei Y. Kitaev
4. S. Shenker
5. G. Turiaci
6. Tom Mertens
7. S. J. Suh
8. Jordan S. Cotler

In Nuclear and High Energy Physics

1. D. Stanford
2. J. Maldacena
3. V. Rosenhaus
4. Phil Saad
5. Tom Mertens
6. E. Witten
7. Alexei Y. Kitaev
8. G. Turiaci

Citations in the corpus

• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, methodology): “Variants of the SYK model have been studied in [29, 30, 31, 32, 33, 34, 35].”
• Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity (2016, methodology): “rocess (vii) is feasible. It has been also suggested that the degeneracy of the ground state in the SYK model can be read off from the low-temperature behavior of the single-particle Green’s functions [31], Gi,j(t) = hˆc † j(t)ˆci(0)i. (24) We suggest that Gi,j(t) can be measured in a way very simila”
• Power-law out of time order correlation functions in the SYK model (2017, methodology): “At low excitation energies it exhibits an asymptotically exact conformal symmetry [2, 3, 4, 5] which manifests itself in the infinite-dimensional freedom to re-parameterize time, t → f (t), in the description of long time correlations.”
• Three dimensional view of the SYK/AdS duality (2017, unknown): “One does not expect a spin glass state in this model [7] so that we can restrict to the replica diagonal subspace [10].”
• Higher dimensional generalizations of the SYK model (2016, background): “This is simply the sum over the replicated action obtained for each site separately, for a direct comparison see for example the discussion in [6, 15].”
• Chaos in quantum channels (2015, methodology): “fast scramblers in the sense of [2], such as the Majorana fermion model of Kitaev [11] (a simplification of the Sachdev-Ye model of N SU(M) spins [26], see also [27]) or a large N strongly interacting CFT holographically dual to Einstein gravity near its Hawking-Page point.”
• Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models (2018, methodology): “Our discussion will closely follow the treatment described in detail in previous work on SYK models [46,51,67].”
• A generalization of Sachdev-Ye-Kitaev (2016, background): “For one flavor, this reduces to the effective action for SYK [2] (see [1] for an analogous expression for the SY model, and [18] for the Dirac fermion version of SYK).”
• Numerical study of fermion and boson models with infinite-range random interactions (2016, background): “(16) Then we have P (τ, τ ′) = G(τ ′, τ), (17) and the saddle point solution becomes G(iωn) = 1 iωn + μ− Σ(iωn) Σ(τ) = −J(2)G(2)(τ)G(−τ) (18) The above equation shows a re-parameterization symmetry at low temperature if we ignore the iωn term [9, 10].”
• Bi-local holography in the SYK model (2016, unknown): “Their solution (and earlier works [5, 7]) employ the emergent conformal symmetry of the model and correspondingly exhibit characteristic features of the AdS theory.”
• Bi-local holography in the SYK model: perturbations (2016, background): “We do not expect a spin glass state in this model [7] and we can restrict to replica diagonal subspace [15].”
• Notes on the complex Sachdev-Ye-Kitaev model (2019, methodology): “he zero temperature entropy in Eq. (1.11) and the pair of soft modes as in Eq. (1.12) are also pertinent to higher dimensional charged black holes with AdS 2 horizons, and this is discussed elsewhere [9,3,10{12,8,13{18]. Key aspects of such black holes are summarized in AppendixG. We also note that ”
• Black holes and random matrices (2016, methodology): “The action (16) is obtained by performing the disorder average over couplings Jijkl, introducing a HubbardStratonovich field for the fermion bi-linear, and integrating out the fermions [7, 46].”
• Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models (2016, background): “We argue that this model is related in the large N limit to the generalization of SYK model which contains complex fermions [36, 37].”