Abstract
Abstract We continue our recently proposed holographic description of single-particle correlation functions for four-dimensional chiral fermions with Lifshitz scaling at zero chemical potential, paying particular attention to the dynamical exponent z = 2. We present new results for the spectral densities and dispersion relations at non-zero momenta and temperature. In contrast to the relativistic case with z = 1, we find the existence of a quantum phase transition from a non-Fermi liquid into a Fermi liquid in which two Fermi surfaces spontaneously form, even at zero chemical potential. Our findings show that the boundary system behaves like an undoped Weyl semimetal.
Highlights
Over the past years, the AdS/conformal field theory (CFT) correspondence has become a more and more popular and widespread tool which offers the opportunity to apply ideas from string theory to realistic materials studied in condensed-matter physics, see e.g. [1,2,3,4,5] and references therein
We continue our recently proposed holographic description of single-particle correlation functions for four-dimensional chiral fermions with Lifshitz scaling at zero chemical potential, paying particular attention to the dynamical exponent z = 2
In contrast to the relativistic case with z = 1, we find the existence of a quantum phase transition from a non-Fermi liquid into a Fermi liquid in which two Fermi surfaces spontaneously form, even at zero chemical potential
Summary
The AdS/CFT correspondence has become a more and more popular and widespread tool which offers the opportunity to apply ideas from string theory to realistic materials studied in condensed-matter physics, see e.g. [1,2,3,4,5] and references therein. The retarded single-particle correlation or Green’s function GR is measurable in electronic systems using angle-resolved photoemission spectroscopy (ARPES) For this reason, we are interested in finding GR of a strongly interacting condensed-matter system using holographic methods. By computing the momentum distribution of the particles and holes, we find for z = 1 that our holographic model for a Weyl semimetal contains a quantum phase transition between a non-Fermi-liquid phase and a Fermi-liquid phase with two Fermi surfaces, one for the particles and one for the holes, even at zero doping. One can think of 1/λ as a spin-orbit coupling constant and of g as an effective interaction parameter coupling the elementary fermion to the conformal field theory These parameters are not present in the standard formulation of holography, but enter our holographic prescription for the fermionic single-particle Green’s function. There are a number of appendices which contain our conventions and give more details about the calculations
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