We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an
AdS2 chain. Specifically, by studying a double-trace deformation of a
Z2 scalar in an
AdS2 chain where the
Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an
AdS2 chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon
AdS2 space-time.
The dissipative dynamics of strongly interacting systems are often characterized by the timescale set by the inverse temperature ${\ensuremath{\tau}}_{P}\ensuremath{\sim}\ensuremath{\hbar}/({k}_{B}T)$. We show that near a class of strongly interacting quantum critical points that arise in the infrared limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) whose lifetime ${\ensuremath{\tau}}_{\mathrm{eq}}$ is parametrically longer than ${\ensuremath{\tau}}_{P}$: ${\ensuremath{\tau}}_{\mathrm{eq}}\ensuremath{\gg}{T}^{\ensuremath{-}1}$. The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point. The thermal diffusivity (in units of the butterfly velocity) is anomalously large near the quantum critical point and is governed by ${\ensuremath{\tau}}_{\mathrm{eq}}$ rather than ${\ensuremath{\tau}}_{P}$. We conjecture that there exists a long-lived, propagating collective mode with velocity
vs, and in this case the relation $D={v}_{s}^{2}{\ensuremath{\tau}}_{\mathrm{eq}}$ holds exactly in the limit $T{\ensuremath{\tau}}_{\mathrm{eq}}\ensuremath{\gg}1$. While scale invariance is broken, a generalized scaling theory still holds provided that the dependence of observables on the dangerously irrelevant coupling is incorporated. Our work further underlines the connection between dangerously irrelevant deformations and slow equilibration.
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 .
We identify the universal mechanism behind the thermalization of (1+1)d QFTs at high and low temperatures. Viewing these theories as CFTs perturbed by relevant or irrelevant deformations, we show that conformal perturbation theory in the thermal state breaks down at late times allowing for the emergence of hydrodynamics. This breakdown occurs universally due to the unsuppressed exchange of stress tensors near the lightcone. Furthermore, for theories with central charge c→∞ c → ∞ we solve for the emergent hydrodynamic theory to all orders in the gradient expansion by arguing that all transport parameters appearing in two-point functions have universal expressions in terms of the scaling dimension \Delta Δ of the perturbation. The radius of convergence of the hydrodynamic dispersion relations provides an early time cutoff for hydrodynamics, which agrees with the time scale at which conformal perturbation theory breaks down.
We study thermodynamic and transport observables of quantum critical states that arise in the infrared limit of holographic renormalization group flows. Although these observables are expected to exhibit quantum critical scaling, there are a number of cases in which their frequency and temperature dependences are in apparent contradiction with scaling theories. We study two different classes of examples and show in both cases that the apparent breakdown of scaling is a consequence of the dependence of observables on an irrelevant deformation of the quantum critical state. By assigning scaling dimensions to the near-horizon observables, we formulate improved scaling theories that are completely consistent with all explicit holographic results once the dependence on the dangerously irrelevant coupling is properly accounted for. In addition to governing thermodynamic and transport phenomena in these states, we show that the dangerously irrelevant coupling also controls late-time equilibration, which occurs at a rate parametrically slower than the temperature $1/{\ensuremath{\tau}}_{\mathrm{eq}}\ensuremath{\ll}T$. At very late times, transport is diffusion-dominated, with a diffusivity that can be written simply in terms of ${\ensuremath{\tau}}_{\mathrm{eq}}$ and the butterfly velocity, $D\ensuremath{\sim}{v}_{B}^{2}{\ensuremath{\tau}}_{\mathrm{eq}}$. We conjecture that in such cases there exists a long-lived, propagating collective mode with velocity
vs, and in this case the relation $D={v}_{s}^{2}{\ensuremath{\tau}}_{\mathrm{eq}}$ holds exactly in the limit ${\ensuremath{\tau}}_{\mathrm{eq}}T\ensuremath{\gg}1$.
Quantum phase transitions occur strictly at zero temperature and are accessed by varying a physical parameter such as a magnetic field or chemical potential. While these transitions themselves are experimentally inaccessible, the existence of a zero temperature quantum critical point has remarkable effects on the dynamical properties of interacting quantum many-body systems at finite temperatures. In this thesis, we study dynamics in four strongly interacting many-body systems near quantum critical points in the context of NMR relaxation, quantum quenches, many-body quantum chaos, and charge diffusion. In chapter 1, we begin by revisiting the issue of NMR relaxation in the quantum disordered phase of Ising spin chains. We find that the imaginary part of the spin susceptibility at low frequences is dominated by rare quantum processes which leads to an NMR relaxation rate that scales as
1/T1∼exp(−T2Δ) near the quantum critical point rather than the previously conjectured
1/T1∼exp(−TΔ). These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system
CoNb2O6. In chapter 2, we study the non-equilibrium dynamics of Sachdev-Ye-Kitaev (SYK) models with
q body interactions after a quantum quench, considering a quench protocol which drives the system from an initial state with long-lived quasiparticle excitations to a final state lacking any long-lived quasiparticle excitations. For
q=4, we find that the timescale for the system to locally thermalize
τeq∼kBTℏ and for
q→∞ we find that the system thermalizes instantaneously. In chapter 3, we study the real time dynamics of quantum electrodynamics in 2+1 dimensions with
Nf flavors of fermions. We focus on thermalization and the onset of many-body quantum chaos and compute the quantum Lyapunov exponent in a
Nf1 expansion. We briefly comment on chaos, locality, and gauge invariance. Finally, in Chapter 4 we consider whether the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals by computing the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength ``hydrodynamic" disorder. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.