Thermal diffusivity and butterfly velocity in anisotropic Q-Lattice models

Abstract

By using a holographic method we study a relation between the thermal diffusivity ($D_T$) and two quantum chaotic properties, Lyapunov time (${\tau }_L$) and butterfly velocity ($v_B$) in strongly correlated systems. It has been shown that $D_T/(v_B^2{\tau }_L)$ is universal in some holographic models as well as condensed matter systems including the Sachdev-Ye-Kitaev (SYK) models. We investigate to what extent this relation is universal in the Q-lattice models with infrared (IR) scaling geometry, focusing on the effect of spatial anisotropy. Indeed it was shown that ${\mathcal{E}}_i:=D_{T,i}/(v_{B,i}^2{\tau }_L)$ ($i=x,y$) is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, in this work, we find the concrete expressions for ${\mathcal{E}}_i$ in terms of the critical dynamical exponents $z_i$ in each direction. By analyzing the IR scaling geometry we identify the allowed scaling parameter regimes, which enable us to compute the allowed range of ${\mathcal{E}}_i$. We find the lower bound of ${\mathcal{E}}_i$ is always $1/2$, which is not affected by anisotropy, contrary to the $\eta /s$ case. However, there may be an upper bound determined by anisotropy.

32 pages, 1 figure, v2: 33 pages, references added

References in corpus (18)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Viscosity Bound and Causality Violation
• Theory of universal incoherent metallic transport
• Quantum Criticality
• Slow scrambling in disordered quantum systems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Thermoelectric DC conductivities from black hole horizons
• Quantum chaos on a critical Fermi surface
• Thermal diffusivity and chaos in metals without quasiparticles
• Coherent/incoherent metal transition in a holographic model
• An upper bound on transport
• Diffusion and Chaos from near AdS${}_2$ horizons
• Holographic RG flow of the shear viscosity to entropy density ratio in strongly coupled anisotropic plasma
• Charge diffusion and the butterfly effect in striped holographic matter
• A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography
• On Butterfly effect in Higher Derivative Gravities
• On the Butterfly Effect in 3D Gravity
• Power Law of Shear Viscosity in Einstein-Maxwell-Dilaton-Axion model

Cited by in corpus (40)

• Holographic Axion Model: a simple gravitational tool for quantum matter
• Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
• Conjecture on the Butterfly Velocity across a Quantum Phase Transition
• Universal Bounds on Transport in Holographic Systems with Broken Translations
• Chaos and entanglement spreading in a non-commutative gauge theory
• Thermal Diffusion and Quantum Chaos in Neutral Magnetized Plasma
• The breakdown of magneto-hydrodynamics near AdS${}_2$ fixed point and energy diffusion bound
• Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states
• Quasi-normal modes of dyonic black holes and magneto-hydrodynamics
• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
• Deep learning bulk spacetime from boundary optical conductivity
• Interplay between the Lyapunov exponents and phase transitions of charged AdS black holes
• Weyl corrections to diffusion and chaos in holography
• Homes' law in holographic superconductor with linear-$T$ resistivity
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points
• Linear-$T$ resistivity at high temperature
• Chaos, Diffusivity, and Spreading of Entanglement in Magnetic Branes, and the Strengthening of the Internal Interaction
• Kasner interiors from analytic hairy black holes
• Upper bound of the charge diffusion constant in holography
• T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
• Lifshitz symmetry: Lie algebras, spacetimes and particles
• The Effect of Anisotropy on Holographic Entanglement Entropy and Mutual Information
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• Diffusivities bounds in the presence of Weyl corrections
• Dynamic Properties of Two-Dimensional Latticed Holographic System
• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
• Linear-$T$ resistivity from low to high temperature: axion-dilaton theories
• Holographic subdiffusion
• Holographic Butterfly Velocities in Brane Geometry and Einstein-Gauss-Bonnet Gravity with Matters
• On pole-skipping with gauge-invariant variables in holographic axion theories
• A novel holographic quantum phase transition and butterfly velocity
• Transverse Goldstone mode in holographic fluids with broken translations
• AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model
• Butterfly Velocity in Quadratic Gravity
• Deep learning-based holography for T-linear resistivity
• Anisotropic critical points from holography
• Nodal-antinodal dichotomy from anisotropic quantum critical continua in holographic models
• Recent developments in the holographic description of quantum chaos
• Shear viscoelasticity in anisotropic holographic axion model