Abstract
We study a holographic model which exhibits a quantum phase transition from the strongly interacting Weyl semimetal phase to an insulating phase. In the holographic insulating phase there is a hard gap in the real part of frequency dependent diagonal conductivities. However, the anomalous Hall conductivity is nonzero at zero frequency, indicting that it is a Chern insulator. This holographic quantum phase transition is always of first order, signified by a discontinuous anomalous Hall conductivity at the phase transition, in contrast to the very continuous holographic Weyl semimetal/trivial semimetal phase transition. Our work reveals the novel phase structure of strongly interacting Weyl semimetal.
Highlights
Have been constructed in [9, 10] in which the anomalous Hall conductivity is an order parameter to characterize the quantum topological phase transition.1 The effects of the surface state [13] and topological invariants [14] in this holographic model exhibit key features of topological Weyl semimetals
This behavior exists for any q0 > 0.9 Notably this is quite different from the previous holographic model [9] in which a continuous holographic phase transition happens between the topological Weyl semimetal phase and a trivial semimetal phase
We have provided a holographic model to charaterize the quantum phase transition between the strongly interacting Weyl semimetal and the Chern insulator, by tunning the ratio between the mass parameter and time reversal symmetry breaking parameter in the dual field theory
Summary
We shall start from the most general holographic system which duals to an anomalous system with U(1)V × U(1)A. With the free parameter φ0, this IR geometry could flow to the whole spacetime asymptotic to AdS5 with different M/b This kind of near horizon shows up in the groundstate of the holographic superconductor [32, 33] and the holographic Weyl semimetal phase studied in [9]. Near the critical value of M/b, we observe oscillatory behavior of the matter fields (dashed color lines), which is due to the complex irrelevant deformations around the Lifshtiz fixed point This can be taken as a signature of unstable critical solution, indicating that the phase transition is not continuous, which will be confirmed from the free energy in the subsection
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