We investigate the breakdown of magneto-hydrodynamics at low temperature ($T$) with black holes whose extremal geometry is AdS$_2times$R$^2$. The breakdown is identified by the equilibration scales ($omega_{text{eq}}, k_{text{eq}}$) defined as the co
llision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show ($omega_{text{eq}}, k_{text{eq}}$) at low $T$ is determined by the diffusion constant $D$ and the scaling dimension $Delta(0)$ of an infra-red operator: $omega_{text{eq}} = 2pi T Delta(0), , k_{text{eq}}^2 = omega_{text{eq}}/D$, where $Delta(0)=1$ in the presence of magnetic fields. For the purpose of comparison, we have analytically shown $Delta(0)=2$ for the axion model independent of the translational symmetry breaking pattern (explicit or spontaneous), which is complementary to previous numerical results. Our results support the conjectured universal upper bound of the energy diffusion $D ,le, omega_{text{eq}}/k_{text{eq}}^2 ,:=, v_{text{eq}}^2 , tau_{text{eq}}$ where $v_{text{eq}}:= omega_{text{eq}}/k_{text{eq}}$ and $tau_{text{eq}}:=omega_{text{eq}}^{-1}$ are the velocity and the timescale associated to equilibration, implying that the breakdown of hydrodynamics sets the upper bound of the diffusion constant $D$ at low $T$.
We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically ch
arged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($lambda_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D ,geqslant, v_{B}^2/lambda_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.
In this paper we study a hysteric phase transition from weak localization phase to hysteric magnetoconductance phase using gauge/gravity duality. This hysteric phase is triggered by a spontaneous magnetization related to $mathbb{Z}_2$ symmetry and ti
me reversal symmetry in a 2+1 dimensional system with momentum relaxation. We derive thermoelectric conductivity formulas describing non-hysteric and hysteric phases. At low temperatures, this magnetoconductance shows similar phase transitions of topological insulator surface states. We also obtain hysteresis curves of Seebeck coefficient and Nernst signal. It turns out that our impurity parameter plays a role of magnetic impurity. This is justified by showing increasing susceptibility and the spontaneous magnetization with increasing impurity parameter.
We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillato
r. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.
We study (fermionic) spectral functions in two holographic models, the Gubser-Rocha-linear axion model and the linear axion model, where translational symmetry is broken by axion fields linear to the boundary coordinates ($psi_{I}=beta delta_{Ii} x^{
i}$). Here, $beta$ corresponds to the strength of momentum relaxation. The spectral function is computed by the fermionic Greens function of the bulk Dirac equation, where a fermion mass, $m$, and a dipole coupling, $p$, are introduced as input parameters. By classifying the shape of spectral functions, we construct complete phase diagrams in ($m,p,beta$) space for both models. We find that two phase diagrams are similar even though their background geometries are different. We also find that the effect of momentum relaxation on the (spectral function) phases of two models are similar even though the effect of momentum relaxation on the DC conductivities of two models are very different. We suspect that this is because holographic fermion does not back-react to geometry in our framework.
We study the spontaneous magnetization and the magnetic hysteresis using the gauge/gravity duality. We first propose a novel and general formula to compute the magnetization in a large class of holographic models. By using this formula, we compute th
e spontaneous magnetization in a model like a holographic superconductor. Furthermore, we turn on the external magnetic field and build the hysteresis curve of magnetization and charge density. To our knowledge, this is the first holographic model realizing the hysteresis accompanied with spontaneous symmetry breaking. By considering the Landau-Ginzburg type effective potential in the symmetry broken phase, we obtain the mass of the magnon from the bulk geometry data.
The linear-$T$ resistivity is one of the characteristic and universal properties of strange metals. There have been many progress in understanding it from holographic perspective (gauge/gravity duality). In most holographic models, the linear-$T$ res
istivity is explained by the property of the infrared geometry and valid at low temperature limit. On the other hand, experimentally, the linear-$T$ resistivity is observed in a large range of temperatures, up to room temperature. By using holographic models related to the Gubser-Rocha model, we investigate how much the linear-$T$ resistivity is robust at higher temperature above the superconducting phase transition temperature. We find that strong momentum relaxation plays an important role to have a robust linear-$T$ resistivity up to high temperature.
Gauge/Gravity duality as a theory of matter needs a systematic way to characterise a system. We suggest a `dimensional lifting of the least irrelevant interaction to the bulk theory. As an example, we consider the spin-orbit interaction, which causes
magneto-electric interaction term. We show that its lifting is an axionic coupling. We present an exact and analytic solution describing diamagnetic response. Experimental data on annealed graphite shows a remarkable similarity to our theoretical result. We also find an analytic formulas of DC transport coefficients, according to which, the anomalous Hall coefficient interpolates between the coherent metallic regime with $rho_{xx}^{2}$ and incoherent metallic regime with $rho_{xx}$ as we increase the disorder parameter $beta$. The strength of the spin-orbit interaction also interpolates between the two scaling regimes.
We investigate the response of dense and hot holographic QCD (hQCD) to a static and baryonic electric field E using the chiral model of Sakai and Sugimoto. Strong fields with E>(sqrtlambda M_{KK})^2 free quark pairs, causing the confined vacuum and m
atter state to decay. We generalize Schwingers QED persistence function to dense hQCD. At high temperature and density, Ohms law is derived generalizing a recent result by Karch and OBannon to the chiral case.
We consider the diffusion of a non-relativistic heavy quark of fixed mass M, in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT duality. The Greens function constructed around a static string embedded in a background with
a moving horizon, is identified with the noise correlation function in a Langevin approach. The (electric) noise decorrelation is of order 1/T(tau) while the velocity de-correlation is of order MD(tau)/T(tau). For MD>1, the diffusion regime is segregated and the energy loss is Langevin-like. The time dependent diffusion constant D(tau) asymptotes its adiabatic limit 2/pisqrt{lambda} T(tau) when tau/tau_0=(1/3eta_0tau_0)^3 where eta_0 is the drag coefficient at the initial proper time tau_0.
