Holographic fermions in charged Lifshitz theory

Abstract

We investigate the properties of holographic fermions in charged Lifshitz black holes at finite temperature through the AdS/CFT correspondence. In the charged Lifshitz background with the dynamical exponent $z=2$, we find that the dispersion relation is linear. The scaling behavior of the imaginal part of the Green function relative to $k_{\perp}=k-k_F$ is also discussed. We find, although the system has linear dispersion relation and quadratic quasi-particle width, it does not satisfy Luttinger's theorem. We also find that the variation of the scaling parameters $\alpha$ and $\beta$ is small as the charge $q$ varies. Furthermore, we also discuss the effect of the dynamical exponent $z$ by considering the cases $z=4$ and $z=6$ and show that $ImG_{ii}$ become smooth when the dynamical exponent $z$ increases.Comment: 1+16pages, many figures, published versio

Charged Lifshitz black hole and probed Lorentz-violation fermions from holography

“…Our results show that, different from the effect of dynamical exponent which suppresses the peak of the fermionic spectral function [36,45], the Lorentz-violation of fermions will enhance the peak and make the fermi momentum larger to compensate the non-relativistic bulk effect. Also, for fixed z, small Lorentz-violation of fermions corresponds the low energy excitation as non-Fermi liquid with nonlinear dispersion relation, when the Lorentz-violation becomes larger than a critical value, the low energy excitation always behaves as Fermi liquid with linear dispersion relation.…”

“…However, the previous works usually started by adding relativistic fermions into the (non-)relativistic bulk theory. Since 1 The generalization of holographic fermions obtain many remarkable progress, such as the effects of different bulk theory on the fermionic correlation [31][32][33][34][35][36][37][38][39][40], holographic non-relativistic fermionic fixed points by imposing the Lorentz violating boundary condition [41][42][43][44][45], phase transition from the Fermi liquid to non-Fermi liquid and also to the Mott insulating phase due to the interaction between Dirac field and gauge field [46][47][48][49][50][51] and the fermionic spectral function effected by lattice effects [52][53][54][55][56], etc.. the anisotropic scaling (1) is built by construction in the HL gravity, it is natural to expect the coupling matters exhibit the same scaling in the same footing. This is the other motivation to introduce the probed non-relativistic fermions into the non-relativistic HL gravity and study the effect of the Lorentz-violation on the Fermionic spectral function.…”

Holographic fermionic spectrum from Born–Infeld AdS black hole

“…Furthermore, they find that this scaling behavior is controlled by conformal dimensions in the IR CFT dual to AdS 2 [4]. Subsequently, a lot of extensive explorations on the Fermi surface structure and associated excitations have also been implemented in more general geometries in [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein. These holographic fermionic systems are expected to be candidates for generalized non-Fermi liquids and offer a possible clue to uncover the basic principle hidden behind the strangle metal phase.…”

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

“…It was showed that the Lifshitz exponent z in the holographic fermion systems plays an important role in the retarded Green's function [23,24]. For a specific value of the critical exponent z, the Luttinger's theorem is violated [25] and even a dynamical gap can be generated in the presence of a dipole coupling [26][27][28].…”