Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography

Abstract

We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number, Q. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low temperature energy and Q fluctuations. We obtain higherdimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of Einstein-Maxwell-axion theories on black brane geometries which interpolate from either AdS 4 or AdS 5 to an AdS 2 × R 2 or AdS 2 × R 3 near-horizon geometry. These provide holographic descriptions of non-quasiparticle metallic states without momentum conservation. We find a precise match between low temperature transport and thermodynamics of the SYK and holographic models. In both models the Seebeck transport coefficient is exactly equal to the Q-derivative of the entropy. For the SYK models, quantum chaos, as characterized by the butterfly velocity and the Lyapunov rate, universally determines the thermal diffusivity, but not the charge diffusivity.

Diffusion and butterfly velocity at finite density

“…More evidence for the energy diffusion bound (D e /v 2 B ) was shown in holographic models that flow to AdS 2 ×R d fixed points in the infrared in [20] and in the Sachdev-Ye-Kitaev (SYK) models [21][22][23]. 4 However, it was shown that charge diffusion (D c /v 2 B ) may not have a universal lower bound in striped holographic matter [24] and in the SYK model [22]. When the higher derivative correction is added the energy diffusion (D e /v 2 B ) still can have a lower bound while the charge diffusion (D c /v 2 B ) may vanish depending on the higher derivative couplings [25].…”

“…3 This idea was first tested at zero density in a class of holographic model with an scaling infrared geometry in [15,19], where concrete examples supporting the bound (1.8) with the butterfly velocity were provided. More evidence for the energy diffusion bound (D e /v 2 B ) was shown in holographic models that flow to AdS 2 ×R d fixed points in the infrared in [20] and in the Sachdev-Ye-Kitaev (SYK) models [21][22][23]. 4 However, it was shown that charge diffusion (D c /v 2 B ) may not have a universal lower bound in striped holographic matter [24] and in the SYK model [22].…”

“…In the coherent regime, the mixing term M (2.4) is important and (ζ, χ) should be taken into account so the energy diffusion constant in the coherent regime will not be universal. By the same reason the charge diffusion constant may not be universal and this non-universality was also observed in [22,24,25] and it seems that chaos is only connected to energy diffusion [18,22]. Therefore, it is an interesting future direction to search a velocity scale for charge diffusion.…”

The bulk dual of SYK: cubic couplings

“…Or, one can consider a Lorentz invariant higher-dimensional bosonic SYK [30]. For other generalizations, see [19,[50][51][52][53][54][55][56][57][58][59]. In addition, in the study of AdS 2 /CFT 1 one must regulate the bulk, introducing a dilaton and turning it into "nearly" AdS 2 .…”

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

“…As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.…”