Bom Soo Kim

Effective Holographic Theories for low-temperature condensed matter systems

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents (γ, δ) that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the (γ, δ) plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when γ = δ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole (γ, δ) plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T = 0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

Schrödinger holography with and without hyperscaling violation

A bstractWe study the properties of the Schrödinger-type non-relativistic holography for general dynamical exponent z with and without hyperscaling violation exponent θ. The scalar correlation function has a more general form due to general z as well as the presence of θ, whose effects also modify the scaling dimension of the scalar operator. We propose a prescription for minimal surfaces of this “codimension 2 holography”, and demonstrate the (d − 1) dimensional area law for the entanglement entropy from (d + 3) dimensional Schrödinger backgrounds. Surprisingly, the area law is violated for d + 1 < z < d + 2, even without hyperscaling violation, which interpolates between the logarithmic violation and extensive volume dependence of entanglement entropy. Similar violations are also found in the presence of the hyperscaling violation. Their dual field theories are expected to have novel phases for the parameter range, including Fermi surface. We also analyze string theory embeddings using non-relativistic branes.

Holographic quantum criticality and strange metal transport

A holographic model of a quantum critical theory at a finite but low temperature and a finite density is studied. The model exhibits non-relativistic z = 2 Schr¨ odinger symmetry and is realized by the anti- de-Sitter-Schwarzschild black hole in light-cone coordinates. Our approach addresses the electrical conductivities in the presence or absence of an applied magnetic field and contains a control parameter that can be associated with quantum tuning via charge carrier doping or an external field in correlated electron systems. The Ohmic resistivity, the inverse Hall angle, the Hall coefficient and magnetoresistance are shown to be in good agreement with experimental results of strange metals at very low temperature. The holographic model also predicts new scaling relations in the presence of a magnetic field.

Lifshitz field theories at non-zero temperature, hydrodynamics and gravity

A bstractWe consider a covariant formulation of field theories with Lifshitz scaling, and analyze the energy-momentum tensor and the scale symmetry Ward identity. We derive the equation of state and the ideal Lifshitz hydrodynamics in agreement with arXiv:1304.7481, where they were determined by using thermodynamics and symmetry properties. We construct the charged ideal Lifshitz hydrodynamics in the generating functional framework as well as in the gravitational holographic dual description. At the first viscous order, an analysis of the entropy current reveals two additional transport coefficients (one dissipative and one dissipationless) compared to the neutral case, contributing to the charge current and to the asymmetric part of the energy-momentum tensor.

Charged Dilatonic Black Holes and their Transport Properties

We briefly explain the consistency conditions imposed on the effective holographic theories, which are parameterized by two real exponents

Properties of Schrödinger black holes from AdS space

(\gamma,\delta)

Strange metallic behaviour and the thermodynamics of charged dilatonic black holes

that control the IR dynamics. The general scaling of DC resistivity with temperature at low temperature and AC conductivity at low frequency across the whole

A deformation of twistor space and a chiral mass term in N = 4 super Yang-Mills Theory

(\gamma,\delta)

Bulk viscosity in holographic Lifshitz hydrodynamics

plane are explained. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for

Hyperscaling violation: a unified frame for effective holographic theories

(2+1)