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 …

Tensor network algorithms: A route map

MC Bañuls - Annual Review of Condensed Matter Physics, 2023 - annualreviews.org
Tensor networks provide extremely powerful tools for the study of complex classical and
quantum many-body problems. Over the past two decades, the increment in the number of …

Equivalence of restricted Boltzmann machines and tensor network states

J Chen, S Cheng, H **e, L Wang, T **ang - Physical Review B, 2018 - APS
The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep
learning. RBM finds wide applications in dimensional reduction, feature extraction, and …

Review on novel methods for lattice gauge theories

MC Banuls, K Cichy - Reports on Progress in Physics, 2020 - iopscience.iop.org
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying
quantum field theories, and has led to impressive achievements. In particular, it significantly …

Tensor network states and geometry

G Evenbly, G Vidal - Journal of Statistical Physics, 2011 - Springer
Tensor network states are used to approximate ground states of local Hamiltonians on a
lattice in D spatial dimensions. Different types of tensor network states can be seen to …

Neural network renormalization group

SH Li, L Wang - Physical review letters, 2018 - APS
We present a variational renormalization group (RG) approach based on a reversible
generative model with hierarchical architecture. The model performs hierarchical change-of …

Positive tensor network approach for simulating open quantum many-body systems

AH Werner, D Jaschke, P Silvi, M Kliesch, T Calarco… - Physical review …, 2016 - APS
Open quantum many-body systems play an important role in quantum optics and condensed
matter physics, and capture phenomena like transport, the interplay between Hamiltonian …

Resonating valence bond states in the PEPS formalism

N Schuch, D Poilblanc, JI Cirac, D Pérez-García - Physical Review B …, 2012 - APS
We study resonating valence bond (RVB) states in the projected entangled pair states
(PEPS) formalism. Based on symmetries in the PEPS description, we establish relations …

Entanglement and tensor network states

J Eisert - arxiv preprint arxiv:1308.3318, 2013 - arxiv.org
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 …

Renormalization group constructions of topological quantum liquids and beyond

B Swingle, J McGreevy - Physical Review B, 2016 - APS
We give a detailed physical argument for the area law for entanglement entropy in gapped
phases of matter arising from local Hamiltonians. Our approach is based on renormalization …