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 …
renormalization group ideas, tensor networks have been revived thanks to quantum …
Quantum convolutional neural networks
Neural network-based machine learning has recently proven successful for many complex
applications ranging from image recognition to precision medicine. However, its direct …
applications ranging from image recognition to precision medicine. However, its direct …
Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator
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 …
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
We review two important non-perturbative approaches for extracting the physics of low-
dimensional strongly correlated quantum systems. Firstly, we start by providing a …
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 …
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
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 …
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
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 …
under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one …
Observation of fractional Chern insulators in a van der Waals heterostructure
Topologically ordered phases are characterized by long-range quantum entanglement and
fractional statistics rather than by symmetry breaking. First observed in a fractionally filled …
fractional statistics rather than by symmetry breaking. First observed in a fractionally filled …
Variational optimization algorithms for uniform matrix product states
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 concepts to construct a variational algorithm for finding ground states of one …
Tangent-space methods for uniform matrix product states
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 …
product states in the thermodynamic limit. We introduce the manifold of uniform matrix …