Emergent Forces from Holographic Tensor Networks and Critical Spin Chains

The AdS/CFT correspondence stipulates a duality between certain quantum critical points (described by CFTs) and certain theories of gravity in one higher spatial dimension. We attempt to find a manifestation of this duality in a concrete lattice setting. In particular, we consider a MERA tensor network model of AdS/CFT providing a mapping between a (1+1)D critical spin model and a (2+1)D bulk theory. Using a combination of numerics and analytics, we show that the emergent bulk theory arising from the optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have 1-particle and 2-particle energy potentials which quantitatively match predictions from general relativity in AdS at long distances. As such, the (2+1)D bulk theory manifests certain features of AdS gravity. We show that the 1-particle and 2-particle energy potentials arise in the tensor network due to the interplay between quantum operator spreading instantiated by the tensor network mapping and the symmetries of the spin model. A key feature of our work is that our tensor network-based dualities can be efficiently implemented in near-term quantum devices.