Abstract
The (2+1)-dimensional static magnetic susceptibility in strong-coupling is studied via a Reissner-Nordstr\"{o}m-AdS geometry. The analyticity of the susceptibility on the complex momentum $\mathfrak{q}$-plane in relation to the Friedel-like oscillation in coordinate space is explored. In contrast to the branch-cuts crossing the real momentum-axis for a Fermi liquid, we prove that the holographic magnetic susceptibility remains an analytic function of the complex momentum around the real axis in the limit of zero temperature, At zero temperature, we located analytically two pairs of branch-cuts that are parallel to the imaginary momentum-axis for large $|\text{Im}\ \mathfrak{q}|$ but become warped with the end-points keeping away from the real and imaginary momentum-axes. We conclude that these branch-cuts give rise to the exponential decay behaviour of Friedel-like oscillation of magnetic susceptibility in coordinate space. We also derived the analytical forms of the susceptibility in large and small-momentum, respectively.
Highlights
Correlated electronic systems, such as the high temperature superconductors or graphene, are characterized by a spectrum of novel static and transport phenomena that cannot be explained by the traditional Fermi liquid theory of Landau and are difficult to explore with ordinary field theoretic techniques
The holographic theory [1,2,3,4,5,6] built on the conjectured gauge/ gravity duality is expected to shed some lights on the nonperturbative physics and to reveal some generic properties pertaining to a strongly-coupled system [7,8,9], such as a
Through the series solution of the Heun equation involved, we show that the complex poles of χð0; qÞ discussed in [17] merge into four branch cuts of square root type at zero temperature, whose trajectories are located analytically
Summary
Correlated electronic systems, such as the high temperature superconductors or graphene, are characterized by a spectrum of novel static and transport phenomena that cannot be explained by the traditional Fermi liquid theory of Landau and are difficult to explore with ordinary field theoretic techniques. Came the work by Blake et al [27], who solved the Einstein-Maxwell equations numerically for the gauge field and metric tensor fluctuations in the Reissner-Nordström-AdS background with a complex momentum and found two lines of poles of αð0; qÞ whose locations tend to be parallel to the imaginary q-axis for large jImqj and bend toward the imaginary axis at lower jImqj. Their numerical solution indicates an exponentially decaying Friedel-like oscillation behavior even at zero temperature.
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