The Pauli exclusion principle at strong coupling: holographic matter and momentum space

Abstract

For free fermions at finite density, the Pauli exclusion principle is responsible for the existence of a Fermi surface and the consequent presence of low energy spectral weight over a finite range of momenta. We investigate the extent to which this effect occurs in strongly interacting quantum matter with a holographic dual. We obtain the low energy current-current spectral weight in two holographic frameworks at finite density: systems exhibiting semi-local quantum criticality (with a low temperature entropy density vanishing like s ∼ T η ), and a probe D3/D5 system. For the semi-local theory with 0 < η < 2 we find a sharp discontinuity in the transverse spectral weight at a nonzero momentum k . The case η = 1 is found to have additional symmetries and is soluble even at nonzero temperature. We show that this case exhibits a robust linear in temperature resistivity in the presence of random charged impurities. For the probe D3/D5 system we find an analytic expression for the low energy spectral weight as a function of momentum. The spectral weight is supported below a specific momentum k and is exponentially suppressed at higher momenta.

(Super)Yang-Mills at finite heavy-quark density

“…The Bekenstein-Hawking formula applied to the metric (3.14a) or (3.18a), after using the relations (3.22), gives for the entropy density 33) with U T the scale associated to the radius of the horizon (and therefore the temperature) r H .…”

“…This is an indication that there are low-energy degrees of freedom at finite momentum, and suggests a fermionic behavior of the dual theory. To obtain this behavior of the spectral density one must consider the z → ∞ limit with z/θ = −1 [32] (see also [33] for another string theory realization in which z/θ = −1 appears). This is precisely the limit in which the IR fixed point of 4+1 SYM theory with external quark density is obtained.…”

FRW cosmologies and hyperscaling-violating geometries: higher curvature corrections, ultrametricity, Q-space/QFT duality, and a little string theory

“…For hyperscaling-violating geometries, the double scaling limit θ → −∞ and z → ∞ with −θ/z = η > 0 fixed has been studied to some extent due to having a spectral density that is not exponentially suppressed [21]. The spacetime is conformal to AdS 2 × R 2 and appears in near-horizon geometries of dilatonic black holes [88], in addition to having other interesting properties [9,89]. However, in our case we would like to keep z finite and take θ → −∞, which does not seem to have been studied.…”

Searching for Fermi surfaces in super-QED

“…Moreover, while the duality has yielded many striking results, it has also produced many mysteries, such as the fate of Fermi surfaces at strong coupling, explored in e.g. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The 'microscopic' field content of the theories with gravity duals generally includes gauge bosons, fermions, and scalars, with the number of degrees of freedom for all of these scaling as O(N 2 ) in the 4D field theory examples.…”

“…Specifically, we will explore the behavior of N = 1 super-QED (sQED) and N = 2 sQED in the presence of chemical potentials at zero temperature. Even these simple toy models show some curious features, since from a condensed-matter point of view they have unusual field content and interactions, with the 3 In [24] it is observed that density-density correlation functions in theories with dual Lifshitz geometries [29,30] with z = ∞ have momentum-space singularities which suggest the presence of a Fermi surface, but z < ∞ examples do not.…”