Minding the gap in holographic models of interacting fermions

Abstract

We study the holographic dual of fermions interacting in a Schwarzschild-AdS d+1 background via a dipole (Pauli) coupling sourced by a probe gauge field. We find quite generally that a gap forms in the dual operator spectrum as the Pauli coupling is strengthened. Previous investigations have observed this behavior in analogous constructions with Reissner-Nordström-AdS (RN-AdS4) backgrounds, but the emergence of log-oscillatory behavior in those models' spectra prevented identification of the underlying gapping mechanism. Our model obviates this issue through its modified geometry and traces the gapping mechanism back to the bulk dynamics. We show in general that there is a duality between zeros for large positive values of the coupling and poles in the spectrum for equivalent couplings but with opposite sign as seen recently in the RN-AdS4 background 1 . The duality arises from the two possible quantizations for computing the retarded propagator. Coupled with the earlier string results 2,3 that Fermi surfaces are generally absent from the spectral function, our finding that the Pauli term engineers the gap suggests that the model examined here offers a way of studying non-perturbative physics in fermionic matter at finite density typified by Mott insulating systems.

Formation of Fermi surfaces and the appearance of liquid phases in holographic theories with hyperscaling violation

“…These results had stimulated further studies [9][10][11][12][13][14][15][16] on the behaviour of the dipole coupling. A remarkable property was observed in [17] where it was found that there exists a duality between zeroes and poles in holographic systems with massless fermions and a dipole coupling and this property was also verified in [18].…”

Characterizing featureless Mott insulating state by quasiparticle interference: A dynamical mean field theory view

“…In fact, any theory having an electron self energy with a diverging behavior at low frequency is likely to have a non-zero eV c . From the Dyson's equation, the self energy can be expressed as Σ = G graphic models 40,41 . As a result, it is expected that the same result will be obtained if these theories could be incorporated into T -matrix formalism to compute QPIs.…”

Beyond Particles: Unparticles in Strongly Correlated Electron Matter

“…Such a term is well known to give rise to the anomalous magnetic moment of the electron in flat space. Even if the details of the bulk spacetime vary from Reissner-Nordstrom 32,33 to Schwarzschild 34 , as long as the spacetime at the boundary is asymptotically anti de Sitter, the fermionic propagator is gapped [32][33][34] as shown in Fig. (5) once p exceeds a critical value.…”

“…What this suggests is that within the general framework of the gauge-gravity duality, it should be possible to add various terms to the bulk gravity model which couple to the scaling dimension of the dual fermionic operators at the boundary to engineer propagators that exhibit zeros. Indeed, such a construction is possible [32][33][34] . Computing fermionic correlators at the boundary requires fermionic fields in the bulk described by an appropriate equation of motion.…”

“…(5) once p exceeds a critical value. The origin of the gap is now well understood 33,34 and stems from an exact duality…”