Abstract
We consider a holographic fermionic system in which the fermions are interacting with a U(1) gauge field in the presence of a dilaton field in a gravity bulk of a charged black hole with hyperscaling violation. Using both analytical and numerical methods, we investigate the properties of the infrared and ultaviolet Green's functions of the holographic fermionic system. Studying the spectral functions of the system, we find that as the hyperscaling violation exponent is varied, the fermionic system possesses Fermi, non-Fermi, marginal-Fermi and log-oscillating liquid phases. Various liquid phases of the fermionic system with hyperscaling violation are also generated with the variation of the fermionic mass. We also explore the properties of the flat band and the Fermi surface of the non-relativistic fermionic fixed point dual to the hyperscaling violation gravity.
Highlights
One noticeable application of the gauge/gravity application to CM physics is the study of the many-body system at finite charge density
We explore the properties of the flat band and the Fermi surface of the non-relativistic fermionic fixed point dual to the hyperscaling violation gravity
When m ≤ −0.4, δ = 1, which is a linear dispersion relation. It indicates that there is a transition from non-Fermi liquid to Fermi liquid as the m decreases in holographic fermionic system with a RN-AdS black hole in its dual gravity bulk
Summary
To probe the geometry with hyperscaling violation, we consider the following Dirac action including the bulk minimal coupling between the fermion and the gauge field. Dirac equation in Fourier space (√grrΓr∂r − m)F − i(ω + qAt) gttΓtF + ik√gxxΓxF = 0. A Fourier transformation F = F e−iωt+ikixi. QAt) the above equations can be brought in the form of a flow equation of ξI (∂r + 2m√grr)ξI − v + (−1)I k grr gxx v − (−1)I k grr gxx ξI2 = 0. For the convenience of numerical calculation later, we can make a transformation r = 1/u, so that the flow equation (3.7) can be rewritten as f. Since the IR geometry of the charged geometry with hyperscaling violation is AdS2 ×.
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