Related papers: Hyper-invariant tensor networks and holography
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, which conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
A longstanding enigma within AdS/CFT concerns the entanglement entropy of holographic quantum fields in Rindler space. The vacuum of a quantum field in Minkowski spacetime can be viewed as an entangled thermofield double of two Rindler…
In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state $|\Psi\rangle$ using random tensor…
As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from…
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…
We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo effect is the screening of a magnetic impurity coupled anti-ferromagnetically to a bath…
We discuss the Penrose limit of pure AdS space, which is flat Minkowski space. Even though there is no holographic principle, we construct a ``holographic screen'' on which information on the corresponding CFT is encoded. The screen is…
We present a new method of deriving the geometry of entanglement wedges in holography directly from conformal field theories (CFTs). We analyze an information metric called the Bures metric of reduced density matrices for locally excited…
We define a novel class of tensor networks motivated by the Python's Lunch Conjecture (PLC) in local tensor network models of the black hole interior. We start from the observation that, for extended black brane states with short-range…
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…
In this thesis, I study Interface Conformal Field Theories (ICFT) and their holographic dual, which is composed of two asymptotically Anti-de-Sitter (AdS) spaces glued through a thin gravitating membrane. I restrict the study to simple…
In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to a given configuration of matter fields and the metric on a spatial slice. These wavefunctionals must obey a set of constraints as a…
We have investigated a holographic model of a multi-layered superconductor in (2+1)-dimensions using the AdS/CFT correspondence. This correspondence allows us to study strongly interacting condensed matter systems through a weakly…
The holographic principle asserts that the complete description of the interior of a sphere is a theory which not only lives on the surface of the sphere, but also has A/4 binary degrees of freedom. In this context we revisit the question…
We study how coarse-graining procedure of an underlying UV-complete quantum gravity gives rise to a connected geometry. It has been shown, quantum entanglement plays a key role in the emergence of such a geometric structure, namely a smooth…
We present a deep neural network representation of the AdS/CFT correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The…