Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …
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 …
quantum many-body problems. Over the past two decades, the increment in the number of …
Equivalence of restricted Boltzmann machines and tensor network states
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 …
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 …
quantum field theories, and has led to impressive achievements. In particular, it significantly …
Tensor network states and geometry
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 …
lattice in D spatial dimensions. Different types of tensor network states can be seen to …
Neural network renormalization group
We present a variational renormalization group (RG) approach based on a reversible
generative model with hierarchical architecture. The model performs hierarchical change-of …
generative model with hierarchical architecture. The model performs hierarchical change-of …
Positive tensor network approach for simulating open quantum many-body systems
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 …
matter physics, and capture phenomena like transport, the interplay between Hamiltonian …
Resonating valence bond states in the PEPS formalism
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 …
(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 …
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 …
phases of matter arising from local Hamiltonians. Our approach is based on renormalization …