• Corpus ID: 248965100

Superposed Random Spin Tensor Networks and their Holographic Properties

@inproceedings{Langenscheidt2022SuperposedRS,
  title={Superposed Random Spin Tensor Networks and their Holographic Properties},
  author={Simon Langenscheidt},
  year={2022}
}
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to well-defined, discrete geometries on a graph. By applying random tensor averaging techniques, we map entropy calculations to a random Ising model on the same graph, with distribution of couplings determined by the relative sizes of the involved geometries. The… 

References

SHOWING 1-10 OF 45 REFERENCES
Holographic duality from random tensor networks
A bstractTensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of
Quantum gravity states, entanglement graphs and second-quantized tensor networks
Abstract In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a
Holographic maps from quantum gravity states as tensor networks
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop
Bidirectional holographic codes and sub-AdS locality
TLDR
This article proposes a new class of tensor network models that subsume the earlier advances and incorporate additional features of holographic duality, including a holographic interpretation of all boundary states, not just those in a “code” subspace.
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
TLDR
That bulk logical operators can be represented on multiple boundary regions mimics the Rindlerwedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in [1].
Exact holographic mapping and emergent space-time geometry
In this paper, we propose an {\it exact holographic mapping} which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one
The quantum p-spin glass model: a user manual for holographers
We study a large-N bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the p-spin spherical model. Replica symmetry is
Lieb-Robinson bounds and the generation of correlations and topological quantum order.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.
Spin Networks in Nonperturbative Quantum Gravity
A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objects
Spin networks and quantum gravity.
  • RovelliSmolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
TLDR
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.
...
...