Related papers: Advances on Tensor Network Theory: Symmetries, Fer…
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
We investigate entanglement of strongly interacting fermions in spatially inhomogeneous environments. To quantify entanglement in the presence of spatial inhomogeneity, we propose a local-density approximation (LDA) to the entanglement…
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…
In a recent contribution [arXiv:0904:4151] entanglement renormalization was generalized to fermionic lattice systems in two spatial dimensions. Entanglement renormalization is a real-space coarse-graining transformation for lattice systems…
Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their built-in ability of classifying and studying symmetries, and the efficient…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
Entanglement is a central and subtle feature of quantum theory, whose structure and operational behavior can change dramatically when additional physical constraints, such as symmetries or superselection rules, are imposed. Such constraints…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…
Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body…
Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show,…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…
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…
Entanglement in fermion many-body systems is studied using a generalized definition of separability based on partitions of the set of observables, rather than on particle tensor products. In this way, the characterizing properties of…
The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…