Further evidence for lattice-induced scaling

By G. Horowitz, Jorge E Santos, David Tong. 2012

211 citations recorded by the source corpus.

A bstractWe continue our study of holographic transport in the presence of a background lattice. We recently found evidence that the presence of a lattice induces a new intermediate scaling regime in asymptotically AdS4 spacetimes. This manifests itself in the optical conductivity which exhibits a robust power-law dependence on frequency, σ ∼ ω−2/3, in a “mid-infrared” regime, a result which is in striking agreement with experiments on the cuprates. Here we provide further evidence for the existence of this intermediate scaling regime. We demonstrate similar scaling in the thermoelectric conductivity, find analogous scalings in asymptotically AdS5 spacetimes, and show that we get the same results with an ionic lattice.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2dbe37ba0b62076d79a8ed67637c3eadf3b005a4

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Citations in the corpus

General relativity and the cuprates (2013, methodology): “This is exactly the same as what was done for the ionic lattice in [8].”
Momentum dissipation and effective theories of coherent and incoherent transport (2014, result): “When translational symmetry is weakly broken at low energies, momentum is almost-conserved, and the AC conductivities of various holographic models like this have been shown to display Drude-like peaks in agreement with memory matrix predictions [5–15].”
Holographic metals and insulators with helical symmetry (2014, methodology): “In [20, 21] this has been done for RN black-hole type geometries (or more generally geometries that asymptote to those in the IR), while in [22, 23] the analysis has been extended to semilocal hyperscaling violating geometries in the IR.”
A simple holographic model of momentum relaxation (2013, background): “5 An intermediate frequency scaling regime for numerical lattice set-ups was observed in [2, 3].”
Holographic lattice in Einstein-Maxwell-dilaton gravity (2013, methodology): “Especially, in recent work [6, 7], a holographic lattice model has been constructed in the Einstein-Maxwell theory by introducing a periodic scalar field to simulate the lattice, or directly imposing a periodic condition for the chemical potential on the boundary, which is also called as ionic latti”
Universal Resistivity from Holographic Massive Gravity (2013, background): “This can be done perturbatively, viewing the lattice as an irrelevant operator from the IR perspective [5], or more directly by computing charge transport in the background of a spatially modulated bulk [6, 7, 8, 9] or in the presence of impurities [10, 11].”
Holographic Quantum Matter (2016, background): “An additional structure is seen at intermediate frequencies ω ∼ kL, associated with resonances with the modulating potential [135; 391].”
Holographic Q-lattices (2013, background): “For α = π/4 this gives the family Q-lattices that we discussed in this paper, while for α = 0 it gives the lattices discussed in [2] (who just considered m(2) = −2).”
Momentum relaxation in holographic massive gravity (2013, background): “r0µ). (5) behaves like a scaling law with a constant term |σ| = c+Kωγ−2, and an approximately constant phase. Similar behaviour with arobust value ofγ ≈ 1.35was seen in the holographic lattice models [1,2]. In ﬁgure 3 we plot dlog(|σ|− c)/dlogω (which should be a constant equal to γ − 2 if σ is desc”
Numerical methods for finding stationary gravitational solutions (2015, methodology): “a lower-order grid that covers the regions that are less smooth [234, 236, 238, 247, 248, 253, 256].”
Thermoelectric DC conductivities from black hole horizons (2014, background): “This is a significant technical simplification since the black holes can be constructed by solving ODEs instead of PDEs2 as in the constructions [15, 18–22].”
The thermoelectric properties of inhomogeneous holographic lattices (2014, methodology): “We will see the appearance of a coherent Drude-type peak in the AC conductivity, as in [5], but we will not see any evidence for an intermediate scaling regime that was reported in [5].”