Talks

In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure. We develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all q-body interactions. We derive the full operator growth structure in the large q limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.

I will present a new method to constrain the quantum effective action of gravity, inspired by recent results from causal dynamical triangulations (CDT). After a short introduction to CDT, I will start from a parameterisation of the effective action to calculate correlation functions for observable quantities. Matching these correlators to CDT data allows to reverse-engineer the couplings which describe the effective dynamics. As a concrete example, the autocorrelation of spatial volume fluctuations is considered. The comparison to CDT data suggests the existence of non-local interaction terms, which might have interesting phenomenological consequences for the interpretation of dark energy.

It is widely known that topological orders have long-range entangled gapped ground states from which nontrivial properties can be extracted. We introduce a new theoretical framework named the information convex, the (convex) set of reduced density matrices of a subsystem in its lowest energy, to characterize topological orders. (1) As a concrete example, we present the calculated topology dependent structure of information convex in the quantum double models and show it reveals properties of bulk anyons and deconfined topological excitations along a gapped boundary, and the condensation rules relating them. (2) As a step towards answering "why the structure of information convex looks that way and whether it has predictive power?" we look into some quantum informational constraints. The topological contribution to von Neumann entropy from each topological excitation type and certain fusion constraints are shown to emerge due to strong subadditivity, assuming fusion multiplicity is encoded in certain topological invariant manner.

I will address a long-standing problem of describing the thermodynamics of an accelerating black hole, concentrating on the special case of slowly accelerating black holes in AdS. The key
ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the string tensions that are responsible for the acceleration of the black hole. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard methods. The dual
energy-momentum tensor can be written as a three-dimensional perfect fluid plus a non-hydrodynamic contribution. Some novel thermodynamic phase behavior related to the black hole acceleration will also be discussed.

Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical. This translates into a certain condition on the symplectic form. We find that gravitational subregions that satisfy this condition are bounded by surfaces of extremal area. We characterise the 'centre variables' of the phase space of the graviton in such subsystems, which can be taken to be the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition works to discard local deformations of the boundary surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension ≥ 2.

Electron-phonon interactions; Schaefer-Wolff transformation; Attractive interactions between electrons mediated by phonons; experimental evidence of superconductivity, Cooper problem.