The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

arXiv:1308.3318v2 [quant-ph] 10 Sep 2013 Page 1 Entanglement and tensor network states
Jens Eisert Dahlem Center for Complex Quantum Systems Freie Universität Berlin, 14195 …

We review different descriptions of many-body quantum systems in terms of tensor product
states. We introduce several families of such states in terms of the known renormalization …

Quantum tensor network states and more particularly projected entangled-pair states
provide a natural framework for representing ground states of gapped, topologically ordered …

It is argued that the partition of a quantum system into subsystems is dictated by the set of
operationally accessible interactions and measurements. The emergence of a multipartite …

We develop a general theory of the relation between quantum phase transitions (QPTs)
characterized by nonanalyticities in the energy and bipartite entanglement. We derive a …

Tensor network representations of many-body quantum systems can be described in terms
of quantum channels. We focus on channels associated with the multiscale entanglement …

We study the structure of topological phases and their boundaries in the projected entangled-
pair states (PEPS) formalism. We show how topological order in a system can be identified …

We introduce a framework for characterizing Matrix Product States (MPS) and Projected
Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how …

Results about entanglement (or modular) Hamiltonians of quantum many‐body systems in
field theory and statistical mechanics models, and recent applications in the context of …