Abstract
At high enough charge density, the homogeneous state of the D3-D7' model is unstable to fluctuations at nonzero momentum. We investigate the end point of this instability, finding a spatially modulated ground state, which is a charge and spin density wave. We analyze the phase structure of the model as a function of chemical potential and magnetic field and find the phase transition from the homogeneous state to be first order, with a second-order critical point at zero magnetic field.
Highlights
Is useful for studying the properties of spatially ordered systems but does not say much about how the symmetry became broken in the first place
Comparing with the homogeneous phase, this striped phase is thermodynamically preferred at sufficiently large charge density and small magnetic field
One of the main results of this paper is that the fermion bi-linear cψ will be modulated, resulting in a modulated magnetization, which we identify as a spin density wave
Summary
We begin by setting up the notation and recalling the model under study. We are interested in a holographic quantum liquid modeled by a probe D7-brane embedded in a black D3-brane background. ∞) of the bulk fields ψ, z, a0, ay, as well as the fluxes f1 and f2, together with the parameter rT of the background which is proportional to the temperature. We can freely set the boundary values of z and ay to zero since neither z nor ay enter in the equations of motion without derivatives and they do not have IR constraints. This is unlike for the case of a0, whose IR value has to vanish at the horizon, leaving the UV boundary value a0(r → ∞) ≡ μ as a physical parameter of the theory. To streamline the discussion and because they are quite lengthy, we will not write the equations of motion down explicitly
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