Related papers: Hyper-invariant tensor networks and holography
We study the existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) symmetry. As discrete implementations of the anti de-Sitter/conformal field theory (AdS/CFT) correspondence, such networks have created…
We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do…
The multi-scale entanglement renormalization ansatz (MERA) is a tensor network representation for ground states of critical quantum spin chains, with a network that extends in an additional dimension corresponding to scale. Over the years…
In the holographic correspondence of quantum gravity, a global onsite symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary onsite symmetries can be gauged within…
Central to the AdS/CFT correspondence is a precise relationship between the curvature of an anti-de Sitter (AdS) spacetime and the central charge of the dual conformal field theory (CFT) on its boundary. Our work shows that such a…
The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…
The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. The extra dimension represents the scale of the RG transformation in the field theory. It has been conjectured that the tensor networks…
Holographic quantum error-correcting codes, often realized through tensor network architectures, have emerged as compelling toy models for exploring bulk-boundary duality in AdS-CFT. By encoding bulk information into highly entangled…
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and…
Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network -…
This study examines the holographic representation of the quantum theory of transmission lines, which play a crucial role in quantum computing and quantum information. Utilizing Yurke and Denker's quantum circuit network theory within the…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called…
The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de…
Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretize gravity to incorporate it, because that would…
We derive the multiscale entanglement renormalization ansatz (MERA) for the single impuity Kondo model. We find two types of hidden quantum entanglement: one comes from a finite-temperature effect on the geometry of the MERA network, and…
In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat spacelike boundary,…
We introduce a novel momentum space entanglement renormalization group (MERG) scheme for the topologically ordered (T.O.) ground state of the 2D Hubbard model on a square lattice (\cite{anirbanmotti,anirbanmott2}) using a unitary quantum…