Random matrix product state models of gravitationally prepared states
Gravitationally prepared states are quantum field theoretic states prepared by gravitational path integrals with spatial boundaries that have fixed boundary conditions for gravity but not for matter fields. They can be interpreted as quantum field theoretic states of closed universes encoding quantum gravitational effects of the past. We propose a method of modelling gravitationally prepared states in two dimensions with random matrix product states (RMPS). Such RMPS models allow us to exactly define and compute contributions of higher topologies and replica geometries in the gravitationally prepared state to all orders. We show that the bra-ket wormhole phase transition, a crucial physical property of gravitationally prepared states, is ensured if the transfer matrix of the RMPS satisfies the spectral gapping property, which we define, and define a class of models called $\mathrm{O}(k)$ models satisfying this property. A novel advantage of RMPS models is that they allow us to compute the effects of off-shell wormholes, i.e., wormhole topologies without semiclassical solutions. In particular, using RMPS models, we find that off-shell wormholes lead to nonzero long-distance correlators in gravitationally prepared states. We also define RMPS models in continuous space, and discuss implications for studying de Sitter gravitationally prepared states.