Abstract
We study an anisotropic holographic bottom-up model displaying a quantum phase transition (QPT) between a topologically trivial insulator and a non-trivial Weyl semimetal phase. We analyze the properties of quantum chaos in the quantum critical region. We do not find any universal property of the Butterfly velocity across the QPT. In particular it turns out to be either maximized or minimized at the quantum critical point depending on the direction of propagation. We observe that instead of the butterfly velocity, it is the dimensionless information screening length that is always maximized at a quantum critical point. We argue that the null-energy condition (NEC) is the underlying reason for the upper bound, which now is just a simple combination of the number of spatial dimensions and the anisotropic scaling parameter.
Highlights
The aim of this paper is to understand the onset of quantum chaos across a quantum phase transition in more complicated holographic models displaying a quantum phase transition
We study an anisotropic holographic bottom-up model displaying a quantum phase transition (QPT) between a topologically trivial insulator and a non-trivial Weyl semimetal phase
We argue that the null-energy condition (NEC) is the underlying reason for the upper bound, which now is just a simple combination of the number of spatial dimensions and the anisotropic scaling parameter
Summary
We begin by reviewing the holographic model of [7, 8] which exhibits a QPT from a topologically non-trivial Weyl semimetal to a trivial insulating phase. The hope is that they share the same set of symmetries, thereby capturing the essential properties of the phase transition, if not all the details of the transport pertaining to interacting physics. Note that this is a phase transition in a certain topological invariant (such as Chern number) and not in the symmetries; one can not probe it through the free energy density as it never depends on any topological term in the action. The order parameter is represented by the anomalous Hall conductance, σAHE which is zero in the trivial gapped phase and finite in the Weyl semimetal phase
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