State dependent spread of entanglement in relatively local Hamiltonians

Abstract

Relatively local Hamiltonians are a class of background independent non-local Hamiltonians from which local theories emerge within a set of short-range entangled states. The dimension, topology and geometry of the emergent local theory is determined by the initial state to which the Hamiltonian is applied. In this paper, we study dynamical properties of a simple relatively local Hamiltonian for N scalar fields in the large N limit. It is shown that the coordinate speeds at which entanglement spreads and local disturbance propagates in space strongly depend on state in the relatively local Hamiltonian.

30 pages, 12 figures; v4) a new section on roadmap to quantum gravity + minor corrections

References in corpus (6)

• Towards a derivation of holographic entanglement entropy
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantum Graphity: a model of emergent locality
• Light-cone velocities after a global quench in a non-interacting model
• Emergent Gravity requires (kinematic) non-locality
• Emergent gravity from relatively local Hamiltonians and a possible resolution of the black hole information puzzle

Cited by in corpus (3)

• A model of quantum gravity with emergent spacetime
• Clock-dependent spacetime
• Information propagation in a non-local model with emergent locality