Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

JI Cirac, D Perez-Garcia, N Schuch, F Verstraete - Reviews of Modern Physics, 2021 - APS
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

A practical introduction to tensor networks: Matrix product states and projected entangled pair states

R Orús - Annals of physics, 2014 - Elsevier
This is a partly non-technical introduction to selected topics on tensor network methods,
based on several lectures and introductory seminars given on the subject. It should be a …

Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms

S De Léséleuc, V Lienhard, P Scholl, D Barredo… - Science, 2019 - science.org
The concept of topological phases is a powerful framework for characterizing ground states
of quantum many-body systems that goes beyond the paradigm of symmetry breaking …

Entanglement spectrum of a topological phase in one dimension

F Pollmann, AM Turner, E Berg, M Oshikawa - Physical Review B—Condensed …, 2010 - APS
We show that the Haldane phase of S= 1 chains is characterized by a double degeneracy of
the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the …

Gapped phases with non-invertible symmetries:(1+ 1) d

L Bhardwaj, LE Bottini, D Pajer, S Schäfer-Nameki - SciPost Physics, 2025 - scipost.org
We propose a general framework to characterize gapped infra-red (IR) phases of theories
with non-invertible (or categorical) symmetries. In this paper we focus on (1+ 1) d gapped …

Long-range entanglement from measuring symmetry-protected topological phases

N Tantivasadakarn, R Thorngren, A Vishwanath… - Physical Review X, 2024 - APS
A fundamental distinction between many-body quantum states are those with short-and long-
range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits …

Classification of gapped symmetric phases in one-dimensional spin systems

X Chen, ZC Gu, XG Wen - Physical Review B—Condensed Matter and …, 2011 - APS
Quantum many-body systems divide into a variety of phases with very different physical
properties. The questions of what kinds of phases exist and how to identify them seem hard …

Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization …

S Moudgalya, N Regnault, BA Bernevig - Physical Review B, 2018 - APS
We obtain multiple exact results on the entanglement of the exact excited states of
nonintegrable models we introduced in Phys. Rev. B 98, 235155 (2018) 10.1103/PhysRevB …

Topological phases of fermions in one dimension

L Fidkowski, A Kitaev - Physical Review B—Condensed Matter and Materials …, 2011 - APS
In this paper we show how the classification of topological phases in insulators and
superconductors is changed by interactions, in the case of one-dimensional systems. We …

Hand-waving and interpretive dance: an introductory course on tensor networks

JC Bridgeman, CT Chubb - Journal of physics A: Mathematical …, 2017 - iopscience.iop.org
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 …