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Register a new userFormation of Fermi surfaces and the appearance of liquid phases in holographic theories with hyperscaling violation
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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 Greens 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.
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We employ the numerical and analytical methods to study the effects of the hyperscaling violation on the ground and excited states of holographic superconductors. For both the holographic s-wave and p-wave models with the hyperscaling violation, we observe that the excited state has a lower critical temperature than the corresponding ground state, which is similar to the relativistic case, and the difference of the dimensionless critical chemical potential between the consecutive states decreases as the hyperscaling violation increases. Interestingly, as we amplify the hyperscaling violation in the s-wave model, the critical temperature of the ground state first decreases and then increases, but that of the excited states always decreases. In the p-wave model, regardless of the the ground state or the excited states, the critical temperature always decreases with increasing the hyperscaling violation. In addition, we find that the hyperscaling violation affects the conductivity $sigma$ which has $2n+1$ poles in Im[$sigma$] and $2n$ poles in Re[$sigma$] for the $n$-th excited state, and changes the relation in the gap frequency for the excited states in both s-wave and p-wave models.
A Vaidya type geometry describing gravitation collapse in asymptotically Lifshitz spacetime with hyperscaling violation provides a simple holographic model for thermalization near a quantum critical point with non-trivial dynamic and hyperscaling violation exponents. The allowed parameter regions are constrained by requiring that the matter energy momentum tensor satisfies the null energy condition. We present a combination of analytic and numerical results on the time evolution of holographic entanglement entropy in such backgrounds for different shaped boundary regions and study various scaling regimes, generalizing previous work by Liu and Suh.
We use holography to study the ground state of a system with interacting bosonic and fermionic degrees of freedom at finite density. The gravitational model consists of Einstein-Maxwell gravity coupled to a perfect fluid of charged fermions and to a charged scalar field which interact through a current-current interaction. When the scalar field is non-trivial, in addition to compact electron stars, the screening of the fermion electric charge by the scalar condensate allows the formation of solutions where the fermion fluid is made of antiparticles, as well as solutions with coexisting, separated regions of particle-like and antiparticle-like fermion fluids. We show that, when the latter solutions exist, they are thermodynamically favored. By computing the two-point Green function of the boundary fermionic operator we show that, in addition to the charged scalar condensate, the dual field theory state exhibits electron-like and/or hole-like Fermi surfaces. Compared to fluid-only solutions, the presence of the scalar condensate destroys the Fermi surfaces with lowest Fermi momenta. We interpret this as a signal of the onset of superconductivity.
According to common lore, Equations of State of field theories with gravity duals tend to be soft, with speeds of sound either below or around the conformal value of $v_s=1/sqrt{3}$. This has important consequences in particular for the physics of compact stars, where the detection of two solar mass neutron stars has been shown to require very stiff equations of state. In this paper, we show that no speed limit exists for holographic models at finite density, explicitly constructing examples where the speed of sound becomes arbitrarily close to that of light. This opens up the possibility of building hybrid stars that contain quark matter obeying a holographic equation of state in their cores.
We present an infinite class of 2+1 dimensional field theories which, after coupling to semi-holographic fermions, exhibit strange metallic behavior in a suitable large $N$ limit. These theories describe lattices of hypermultiplet defects interacting with parity-preserving supersymmetric Chern-Simons theories with $U(N) times U(N)$ gauge groups at levels $pm k$. They have dual gravitational descriptions in terms of lattices of probe M2 branes in $AdS_4 times S^7/Z_k$ (for $N gg 1, N gg k^5$) or probe D2 branes in $AdS_4 times CP^3$ (for $N gg k gg 1, N ll k^5$). We discuss several challenges one faces in maintaining the success of these models at finite $N$, including backreaction of the probes in the gravity solutions and radiative corrections in the weakly coupled field theory limit.
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