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Register a new userDiffusion for Holographic Lattices
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Added by
Jerome P. Gauntlett
Publication date
2017
fields
Physics
and research's language is
English
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We consider black hole spacetimes that are holographically dual to strongly coupled field theories in which spatial translations are broken explicitly. We discuss how the quasinormal modes associated with diffusion of heat and charge can be systematically constructed in a long wavelength perturbative expansion. We show that the dispersion relation for these modes is given in terms of the thermoelectric DC conductivity and static susceptibilities of the dual field theory and thus we derive a generalised Einstein relation from Einsteins equations. A corollary of our results is that thermodynamic instabilities imply specific types of dynamical instabilities of the associated black hole solutions.
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In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data {of the dual background black hole solution}. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent $z>2$. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids.
We study black hole solutions of $D=4$ Einstein-Maxwell theory coupled to a charged scalar field that are holographically dual to a $d=3$ conformal field theory with a non-vanishing chemical potential and constant magnetic field. We numerically construct black hole solutions that are dual to a superfluid phase with a periodic lattice of vortices. For the specific model we investigate, we find that the thermodynamically preferred configuration is given by a triangular lattice and moreover the vortices are associated with the lowest Landau level. We also construct black holes describing a lattice of vortices associated with the next to lowest Landau level and while theses are not thermodynamically preferred they exhibit some interesting features that could be realised for other holographic models.
We study the behavior of fermion spectral functions for the holographic topological Weyl and nodal line semimetals. We calculate the topological invariants from the Green functions of both holographic semimetals using the topological Hamiltonian method, which calculates topological invariants of strongly interacting systems from an effective Hamiltonian system with the same topological structure. Nontrivial topological invariants for both systems have been obtained and the presence of nontrivial topological invariants further supports the topological nature of the holographic semimetals.
We study the entanglement entropy in 1+1 dimensional conformal field theories in the presence of interfaces from a holographic perspective. Compared with the well-known case of boundary conformal field theories, interfaces allow for several interesting new observables. Depending on how the interface is located within the entangling region, the entanglement entropies differ and exhibit surprising new patterns and universal relations. While our analysis is performed within the framework of holography, we expect our results to hold more generally.
In a holographic probe-brane model exhibiting a spontaneously spatially modulated ground state, we introduce explicit sources of symmetry breaking in the form of ionic and antiferromagnetic lattices. For the first time in a holographic model, we demonstrate pinning, in which the translational Goldstone mode is lifted by the introduction of explicit sources of translational symmetry breaking. The numerically computed optical conductivity fits very well to a Drude-Lorentz model with a small residual metallicity, precisely matching analytic formulas for the DC conductivity. We also find an instability of the striped phase in the presence of a large-amplitude ionic lattice.
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