Tensor Networks: from Simulations to Holography III

The suitability of tensor network ansatzes for the description of physically relevant states in one dimensional lattice gauge theories (LGT) has been demonstrated in the last years by a large amount of systematic studies, including abelian and non-abelian LGTs, and including scenarios where…

In this talk I will give an overview of tensor network approaches to critical systems. I will discuss entanglement scaling laws, show how PEPS can simulate systems with Fermi surfaces, and present some results for simulating systems in the continuum.

"AdS/CFT endows gravity in anti-de Sitter (AdS) spacetime with a dual description in certain conformal field theories (CFTs) with matching symmetries. Tensor networks on regular discretizations of AdS space provide natural toy models of AdS/CFT, but break the continuous bulk symmetries. In this talk…

There is now significant experimental evidence that the physics of the underdoped cuprates is controlled by a metallic state with a Fermi surface whose volume does not equal the Luttinger value. However, there has been no proposed wavefunction for such a state for electrons in a single band. I will…

Quantum Cellular Automata are unitary maps that preserve locality and respect causality. I will show that in one spatial dimension they correspond to matrix product unitary operators, and that one can classify them in the presence of symmetries, giving rise to phenomenon analogous to symmetry…

"I will introduce a tensor-network based language for classifying topological phases via fixed-point models. The "models" will be tensor networks formalizing a discrete Euclidean path integral living in a topological space-time, and can be obtained from Hamiltonian models by Trotterizing the…

We examine holographic complexity in the doubly holographic model to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near…

Multi-scale tensor networks offer a way to efficiently represent ground states of critical systems and may be adapted for state-preparation on a quantum computer. The tensor network for a single scale specifies a quantum channel whose fixed-point is a subregion of the approximate critical ground…

The search for applications of quantum computers has highlighted the field of quantum chemistry, where one can also apply tensor network methods. There are several challenges in getting useful results for molecules compared to simulating a model Hamiltonian in condensed matter physics. The first…

The success of the Ryu-Takayanagi formula suggests a profound connection between the AdS/CFT correspondence and tensor networks. There are since many works on constructing examples, although it is very difficult to make them explicit and quantitative. We will discuss some new progress in the toy…