Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

@article{Hauschild2018EfficientNS,
  title={Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)},
  author={Johannes Hauschild and F. Pollmann},
  journal={SciPost Physics Lecture Notes},
  year={2018}
}
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-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving… 
TeNeS: Tensor Network Solver for Quantum Lattice Systems
TeNeS (Tensor Network Solver) [1, 2] is a free/libre open-source software program package for calculating two-dimensional many-body quantum states based on the tensor network method. This package
Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States
TLDR
This study presents the discrimination of top quark signal over QCD background processes using a Matrix Product State classifier and shows that entanglement entropy can be used to interpret what a network learns, which can beused to reduce the complexity of the network and feature space without loss of generality or performance.
The ITensor Software Library for Tensor Network Calculations
TLDR
The philosophy behind ITensor, a system for programming tensor network calculations with an interface modeled on tensor diagram notation, and examples of each part of the interface including Index objects, the ITensor product operator, Tensor factorizations, tensor storage types, algorithms for matrix product state (MPS) and matrix product operator (MPO) tensor networks, and the NDTensors library are discussed.
Efficient 2D Tensor Network Simulation of Quantum Systems
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks
TensorTrace: an application to contract tensor networks
TLDR
Emph{TensorTrace} is application designed to alleviate the burden of contracting tensor networks: it provides a graphic drawing interface specifically tailored for the construction of tensor network diagrams, from which the code for their optimal contraction can then be automatically generated.
Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of
Optimization at the boundary of the tensor network variety
TLDR
This work defines a new ansatz class of states that includes states at the boundary of the tensor network variety of given bond dimension and shows how to optimize over this class in order to find ground states of local Hamiltonians by only slightly modifying standard algorithms and code for tensor networks.
The landscape of software for tensor computations
TLDR
The aim is to assemble a comprehensive and up-to-date snapshot of the tensor software landscape, with the intention of helping both users and developers.
Discovering hydrodynamic equations of many-body quantum systems
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system.
Scaling of neural-network quantum states for time evolution
TLDR
It is found that the number of parameters required to represent the quantum state at a given accuracy increases exponentially in time, and the growth rate is only slightly affected by the network architecture over a wide range of different design choices.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 79 REFERENCES
Tensor network states and algorithms in the presence of a global SU(2) symmetry
The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to
Tensor network states and algorithms in the presence of a global SU(2) symmetry
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [Phys.
Tensor network decompositions in the presence of a global symmetry
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to
Tensor Network Renormalization.
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a
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-dimensional quantum
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
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 good place for
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
Abstract A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as well as effective basis sets.
Gauge fixing, canonical forms, and optimal truncations in tensor networks with closed loops
  • G. Evenbly
  • Physics, Mathematics
    Physical Review B
  • 2018
We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized.
Loop Optimization for Tensor Network Renormalization.
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality.
Real-space parallel density matrix renormalization group
We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at
...
1
2
3
4
5
...