We define a relational notion of a subsystem in theories of matrix quantum mechanics and show how the corresponding entanglement entropy can be given as a minimisation, exhibiting many similarities to the Ryu-Takayanagi formula. Our construction brings together the physics of entanglement edge modes, noncommutative geometry and quantum internal reference frames, to define a subsystem whose reduced state is (approximately) an incoherent sum of density matrices, corresponding to distinct spatial subregions. We show that in states where geometry emerges from semiclassical matrices, this sum is dominated by the subregion with minimal boundary area. As in the Ryu-Takayanagi formula, it is the computation of the entanglement that determines the subregion. We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.
I present a consistent theory of classical systems coupled to quantum ones via the path integral formulation. In the classical limit, this is the path integral for stochastic processes like Brownian motion. We apply the formalism to general relativity, since it's reasonable to question whether spacetime should have a quantum nature given its geometric description. In contrast to perturbative quantum gravity, the pure gravity theory is formally renormalisable, and doesn't suffer from negative norm ghosts. This allows for both tabletop experiments and astrophyscical tests of the quantum nature of spacetime.
In this talk I will discuss multi-partite entanglement measures and their computation for holographic theories. I will focus on a particular class of the measures called symmetric measures. If the replica symmetry of the measure is preserved by the bulk solution, then the measure is described by a space with conical singularities whose underlying topology is that of a ball. I will show how such considerations give rise to family multi-partite measures that agree on the holographic state, answering why the holographic states are special.
Characterization of quantum many-body phases through entanglement and non-equilibrium dynamics, such as thermalization, has become a major area of research in recent years. I will discuss calculations of subsystem Renyi entropy in SYK and related models in the large-N limit, mainly based on a new path integral method for computing entanglement entropy of interacting fermions. I will then discuss the non-equilibrium dynamics of SYK models within large-N Schwinger-Keldysh field theory and using finite-N numerics, starting from different types of non-equilibrium initial conditions, like after sudden or slow quenches in the Fermi liquid (FL), non-Fermi liquid (NFL) phases and across NFL-FL transition, as well as starting from a generic pure product state.
