Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Abstract

We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ black hole is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension d, exponents z and θ. Remarkably, the case d = θ and z = 2 is a very special in that the charge diffusion D c is a constant and the energy diffusion D e might be ill-defined, but v 2 B τ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.

Universal bounds on transport in holographic systems with broken translations

“…In simple words, the butterfly velocity v B determines the information scrambling speed in a quantum mechanical system and it can be defined robustly even in absence of quasiparticles. The refined bound: (5) has been tested and discussed in a large number of works especially in connection to black hole physics, holography, quantum information and SYK physics [14,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The final outcome is that, if one considers charge diffusion, the bound in (5) can be violated by considering the effects of inhomogeneity [50] or higher derivative corrections [51], in a way similar to the violation of the conductivity bound of [52], which was shown in [53] and later in [54].…”

New black holes with hyperscaling violation for the transports of quantum critical points with magnetic impurity

“…Therefore, much efforts have been given to the transport calculation in the context of the HSV geometries [31][32][33][34][35][36][37][38][39][40][41][42][43] which seem to be in 1-1 correspondence with the QCP's. However the magneto-thermal conductivity had not been calculated even after a few years of the discovery of exact solution that allows the presence of magnetic field in the context of HSV [39]. The first result on the magneto-heat conductivity was obtained in very recent paper [42] but the result in the zero magnetic field limit does not seem to be reduced to the known result by a parameter dependent factor.…”

Report on scipost_202005_00007v1

“…In simple words, the butterfly velocity v B determines the information scrambling speed in a quantum mechanical system and it can be defined robustly even in absence of quasiparticles. The refined bound: (5) has been tested and discussed in a large number of works especially in connection to black hole physics, holography, quantum information and SYK physics [14,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”