Tensor networks for complex quantum systems

R Orús - Nature Reviews Physics, 2019 - nature.com
Originally developed in the context of condensed-matter physics and based on
renormalization group ideas, tensor networks have been revived thanks to quantum …

Quantum convolutional neural networks

I Cong, S Choi, MD Lukin - Nature Physics, 2019 - nature.com
Neural network-based machine learning has recently proven successful for many complex
applications ranging from image recognition to precision medicine. However, its direct …

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

A Keesling, A Omran, H Levine, H Bernien, H Pichler… - Nature, 2019 - nature.com
Quantum phase transitions (QPTs) involve transformations between different states of matter
that are driven by quantum fluctuations. These fluctuations play a dominant part in the …

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods

AJA James, RM Konik, P Lecheminant… - Reports on Progress …, 2018 - iopscience.iop.org
We review two important non-perturbative approaches for extracting the physics of low-
dimensional strongly correlated quantum systems. Firstly, we start by providing a …

Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy)

J Hauschild, F Pollmann - SciPost Physics Lecture Notes, 2018 - scipost.org
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum
many-body systems in and out of equilibrium. In particular, the one-dimensional matrix …

Signatures of Dirac cones in a DMRG study of the kagome Heisenberg model

YC He, MP Zaletel, M Oshikawa, F Pollmann - Physical Review X, 2017 - APS
The antiferromagnetic spin-1/2 Heisenberg model on a kagome lattice is one of the most
paradigmatic models in the context of spin liquids, yet the precise nature of its ground state …

Time-evolving a matrix product state with long-ranged interactions

MP Zaletel, RSK Mong, C Karrasch, JE Moore… - Physical Review B, 2015 - APS
We introduce a numerical algorithm to simulate the time evolution of a matrix product state
under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one …

Observation of fractional Chern insulators in a van der Waals heterostructure

EM Spanton, AA Zibrov, H Zhou, T Taniguchi… - Science, 2018 - science.org
Topologically ordered phases are characterized by long-range quantum entanglement and
fractional statistics rather than by symmetry breaking. First observed in a fractionally filled …

Variational optimization algorithms for uniform matrix product states

V Zauner-Stauber, L Vanderstraeten, MT Fishman… - Physical Review B, 2018 - APS
We combine the density matrix renormalization group (DMRG) with matrix product state
tangent space concepts to construct a variational algorithm for finding ground states of one …

Tangent-space methods for uniform matrix product states

L Vanderstraeten, J Haegeman… - SciPost Physics Lecture …, 2019 - scipost.org
In these lecture notes we give a technical overview of tangent-space methods for matrix
product states in the thermodynamic limit. We introduce the manifold of uniform matrix …