Abstract
We study the anisotropic properties of dynamical quantities: direct current (DC) conductivity, butterfly velocity, and charge diffusion. The anisotropy plays a crucial role in determining the phase structure of the two-lattice system. Even a small deviation from isotropy can lead to distinct phase structures, as well as the IR fixed points of our holographic systems. In particular, for anisotropic cases, the most important property is that the IR fixed point can be non-AdS2 × ℝ2 even for metallic phases. As that of a one-lattice system, the butterfly velocity and the charge diffusion can also diagnose the quantum phase transition (QPT) in this two-dimensional anisotropic latticed system.
Highlights
JHEP02(2022)119 direction, and the system is an insulating phase in any direction
We study the anisotropic properties of dynamical quantities: direct current (DC) conductivity, butterfly velocity, and charge diffusion
We have studied the anisotropy effect on the dynamical quantities, including the DC conductivity, the butterfly velocity and the charge diffusion
Summary
The holographic Q-lattice model is a concise realization of the periodic structure. Previous holographic lattice models, such as the ionic lattices model and the scalar lattices model, introduce spatially periodic structures on scalar fields or the chemical potential (see [7] for a recent review). The Qlattice model introduces a complex scalar field, which results in only ordinary differential equations. The Aa is the Maxwell field, and φ1,2 is the complex scalar field mimicking the lattice structures. To solve the system (2.1), we need to specify the boundary conditions and system parameters. We set a(0) = 1, At(0) = μ becomes the chemical potential of the dual system. The boundary condition λ1,2 = φ1,2(0) is the strength of the lattice deformation, and k1,2 is the wave vector of the periodic structure. This means that any physical quantity with scaling dimension ∆ will be divided by μ∆ to cancel its scaling dimension
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