We review the appearance of the Planckian time $tau_text{Pl} = hbar/(k_B T)$ in both conventional and unconventional metals. We give a pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize
metals, emphasizing conditions under which these times are the same or different. Throughout, we have attempted to clear up aspects of the problem that had been confusing us, in the hope that this helps the reader as well. We discuss the possibility of a Planckian bound on dissipation from both a quasiparticle and a many-body perspective. Planckian quasiparticles can arise naturally from a combination of inelastic scattering and mass renormalization. Many-body dynamics, on the other hand, is constrained by the basic time- and length- scales of local thermalization.
The room temperature thermal diffusivity of high T$_c$ materials is dominated by phonons. This allows the scattering of phonons by electrons to be discerned. We argue that the measured strength of this scattering suggests a converse Planckian scatter
ing of electrons by phonons across the room temperature phase diagram of these materials. Consistent with this conclusion, the temperature derivative of the resistivity of strongly overdoped cuprates is noted to show a kink at a little below 200 K that we argue should be understood as the onset of a high temperature Planckian $T$-linear scattering of electrons by classical phonons. This kink continuously disappears towards optimal doping, even while strong scattering of phonons by electrons remains visible in the thermal diffusivity, sharpening the long-standing puzzle of the lack of a feature in the $T$-linear resistivity at optimal doping associated to onset of phonon scattering.
The gravitational dual to the grand canonical ensemble of a large $N$ holographic theory is a charged black hole. These spacetimes -- for example Reissner-Nordstrom-AdS -- can have Cauchy horizons that render the classical gravitational dynamics of t
he black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap methodology. I
n this approach, operator expectation values are related by symmetries -- such as time translation and $SU(N)$ gauge invariance -- and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large $N$ single matrix quantum mechanics. Finally, we present new results on the ground state of large $N$ two matrix quantum mechanics.
The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT b
y a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued `near-singularity regime.
We study a family of models for an $N_1 times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single `spherical constra
int. In this way we generalize the results of [1] to a wide class of Ising Hamiltonians with $O(N_1,mathbb{Z})times O(N_2,mathbb{Z})$ symmetry. The models can undergo topological large $N$ phase transitions in which the thermal expectation value of the distribution of singular values of the matrix $S_{aB}$ becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.
High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime $tau gtrsim tau_text{Pl} equiv hbar/(k_B T)$, despite phonon dynamics being entirely classical at these temperatures. W
e argue that this Planckian bound is due to a quantum mechanical bound on the sound velocity: $v_s < v_M$. The `melting velocity $v_M$ is defined in terms of the melting temperature of the crystal, the interatomic spacing and Plancks constant. We show that for several classes of insulating crystals, both simple and complex, $tau/tau_text{Pl} approx v_M/v_s$ at high temperatures. The velocity bound therefore implies the Planckian bound.
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to search for ga
uge invariant low energy states. The ground state, and also long-lived metastable states, of an $mathrm{SU}(N)$ matrix quantum mechanics with three bosonic matrices, as well as its supersymmetric `mini-BMN extension, are studied as a function of coupling and $N$. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geometries in more strongly quantum regimes is probed using the variational wavefunction. We then describe a factorization of the quantum mechanical Hilbert space that corresponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large $N$ limit.
Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this
regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.
Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the out-of-time-ordered correlator in local lattice models. We verify this bound in simu
lations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.
