A bstract The holographic system described by Einstein-Maxwell-Chern-Simons dynamics in the bulk of AdS exhibits a chiral magnetic effect and a quantum critical point. Through numerical calculations, we find that the butterfly velocity can serve as a new identifier for the quantum critical point in this system. We show that the critical point is the point at which the butterfly velocity is equal to the speed of light in the direction of the magnetic field, while in the opposite direction the butterfly propagation vanishes. Furthermore, by studying the pole-skipping points of the response function of the operator dual to the tensor part of the metric perturbation in the bulk, we discover a set of order parameters that distinguish the two states of the system near the quantum critical point. Each of these order parameters is the sum of the absolute values of the real parts of momentum at all pole-skipping points associated with a particular frequency. This quantity vanishes in the disordered state while taking a positive value in the ordered state. In addition, our results confirm the idea that the chiral magnetic effect can manifest macroscopically through quantum chaos.
A bstract The holographic system described by Einstein-Maxwell-Chern-Simons dynamics in the bulk of AdS exhibits a chiral magnetic effect and a quantum critical point. Through numerical calculations, we find that the butterfly velocity can serve as a new identifier for the quantum critical point in this system. We show that the critical point is the point at which the butterfly velocity is equal to the speed of light in the direction of the magnetic field, while in the opposite direction the butterfly propagation vanishes. Furthermore, by studying the pole-skipping points of the response function of the operator dual to the tensor part of the metric perturbation in the bulk, we discover a set of order parameters that distinguish the two states of the system near the quantum critical point. Each of these order parameters is the sum of the absolute values of the real parts of momentum at all pole-skipping points associated with a particular frequency. This quantity vanishes in the disordered state while taking a positive value in the ordered state. In addition, our results confirm the idea that the chiral magnetic effect can manifest macroscopically through quantum chaos.
Abstract We study the butterfly effect and pole-skipping phenomenon for the 1RCBH model which enjoys a critical point in its phase diagram. Using the holographic idea, we compute the butterfly velocity and interestingly find that this velocity can probe the critical behavior of this model. We calculate the dynamical exponent of this quantity near the critical point and find a perfect agreement with the value of the other quantity’s dynamical exponent near this critical point. We also find that at special points, namely the (ω⋆=iλL,k⋆=iλL/vB), (ω⋆=iλL,k⋆=iλL/vB), where λL λL and vB vB are Lyapunov exponent and butterfly velocity respectively, the phenomenon of pole-skipping appears which is a sign of a multivalued retarded Green’s function. Furthermore, we observe that vB2≥cs2 vB2≥cs2 at each point of parameter space of the 1RCBH model where cs cs is the speed of sound wave propagation.
A bstract We analyze pole skipping of stress tensor two-point functions in two-dimensional quantum field theories perturbed away from conformality by a relevant deformation. The retarded two-point Green’s function can be formally computed in conformal perturbation theory, though it results in singular expressions. We propose a natural interpretation of these expressions and compute the resulting Green’s function to leading nontrivial order in the deformation. As a check of our results, we compare the Lyapunov exponents and butterfly velocities we find from our computed skipped poles to those obtained from both a leading-order conformal field theory analysis using Ward identities, as well as to a holographic gravitational dual perturbed by a massive scalar field; we find precise agreement. We comment on extensions to sub-leading order, where agreement with holographic expectations would no longer be expected.
When the Lyapunov exponent λL in a quantum chaotic system saturates the bound λL ≤ 2πk B T , it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).
Abstract Pole skipping is a recently discovered subtle effect in the thermal energy density retarded two point function at a special point in the complex (ω, p) planes. We propose that pole skipping is determined by the stress tensor contribution to many-body chaos, and the special point is at (ω, p)p.s.= iλ(T)(1,1/uB(T)) iλT11/uBT , whereλ(T)= 2π/βand uB(T) uBT are the stress tensor contributions to the Lyapunov exponent and the butterfly velocity respectively. While this proposal is consistent with previous studies conducted for maximally chaotic theories, where the stress tensor dominates chaos, it clarifies that one cannot use pole skipping to extract the Lyapunov exponent of a theory, which obeysλ≤λ(T). On the other hand, in a large class of strongly coupled but non-maximally chaotic theories uB(T) uBT is the true butterfly velocity and we conjecture thatuB≤ uB(T) uBT is a universal bound. While it remains a challenge to explain pole skipping in a general framework, we provide a stringent test of our proposal in the large-qlimit of the SYK chain, where we determineλ, uB, and the energy density two point function in closed form for all values of the coupling, interpolating between the free and maximally chaotic limits. Since such an explicit expression for a thermal correlator is one of a kind, we take the opportunity to analyze many of its properties: the coupling dependence of the diffusion constant, the dispersion relations of poles, and the convergence properties of all order hydrodynamics.
Pole-skipping offers compelling evidence for the hydrodynamic origin of chaotic behavior in strongly coupled quantum systems. We demonstrate that the cumulative effect of higher-order corrections to the hydrodynamic diffusive mode, captured by the parameter Ω, determines the thermal diffusivity through chaos parameters, providing new insights into the interplay between chaos and hydrodynamics. In the incoherent limit, where momentum relaxation is pronounced, we show that the thermodynamically stable phase corresponds to a semi-locally critical IR fixed point. This finding extends previous analyses of simple IR fixed points and may offer a gravity dual description for stable phases beyond the Sachdev-Ye-Kitaev model in the incoherent regime. Additionally, we connect our findings to a universal bound on the thermal diffusion constant in holography , establishing a direct link with the dynamical critical exponent z . We derive a new relation, Ω = ( 2 − z ) / ( 2 z − 2 ) , and propose that it characterizes the thermodynamically stable phase for generic values of z .
Why do black holes emit thermal radiation? And how does a closed quantum system thermalize? These apparently unrelated questions might be both connected to an essential feature of quantum techanics: the dynamics of quantum information and its chaotic properties. Indeed, regardless of the unitary time evolution, quantum information seems to be dissipated. The solution to these contradictions may heavily affect the near future technologies, in light of the recent progresses towards building a quantum computer. In this thesis we investigate the fascinating idea that such chaotic properties leave traces on the late time hydrodynamic excitations. We do this from two opposite directions, both from weakly coupled field theories, using a combination of field theory techniques, and from strongly-coupled field theories, using the AdS/CFT correspondence. Moreover, we studied a fermionic and bosonic quantum critical point, which are 'exotic' states of matter where quantum information plays an important role. The main results of this thesis consist of the formulation of a Boltzmann-like equation for many-body chaos, the discovery of a new property of thermal correlation functions (pole-skipping), and the analysis of which is the correct and meaningful observable to measure experimentally in order to probe quantum chaos.