Tensor Network Python (TeNPy) version 1

Abstract: TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.

• The paper presents TeNPy, a Python library providing a user-friendly yet robust framework for simulating strongly correlated quantum systems, primarily using MPS algorithms for 1D and 2D lattices.
• TeNPy facilitates complex simulations like non-equilibrium dynamics and ground state searches, demonstrated through examples such as a Heisenberg chain and a 2D Ising model simulation.
• Benchmarked favorably against other libraries, TeNPy leverages optimized linear algebra for efficiency and plans future expansions to include non-Abelian symmetries, fermions, GPU support, and broader tensor network types.

Overview of TeNPy: A Python Library for Tensor Network Simulations

The paper presents an in-depth examination of Tensor Network Python (TeNPy), a comprehensive Python library designed for simulating strongly correlated quantum systems using tensor networks. The library is particularly tailored for researchers engaging with matrix product states (MPS) algorithms applied to one-dimensional (1D) and two-dimensional (2D) lattice systems. TeNPy addresses the complexities of quantum simulations with user accessibility in mind, offering both a high level of usability for newcomers and the robustness required by experienced researchers.

Main Features and Functionality

TeNPy is structured into several key subpackages that progressively layer abstraction from high-level simulations to low-level linear algebra operations. The core subpackages include:

1. Simulations: Provides a user-friendly interface for setting up and executing full-scale simulations based on input parameters related to Hamiltonians, system sizes, bond dimensions, and target observables. Notably, support for yaml configuration files enhances reproducibility and simplifies setup.
2. Algorithms: Implements core tensor network algorithms such as DMRG, TEBD, TDVP, and MPO evolution with a focus on modularity and broad applicability. Variations of these algorithms, like single-site and two-site DMRG, are efficiently handled with common algorithmic steps embedded within a shared class hierarchy.
3. Models and Networks: Facilitates the representation of physical lattice models, Hamiltonians, and tensor networks. The generation of MPS and MPO representations is automated, supporting various initialization techniques such as singlet coverings and random evolutions.
4. Linear Algebra: Tenpy implements block-sparse tensor operations, supporting Abelian symmetries and charge conservation. The subpackage offers operations like tensor contractions, eigendecomposition, and singular value decomposition (SVD) with conservation laws taken into account.

Example Applications

In practice, TeNPy enables the simulation of non-equilibrium dynamics and ground state searches in complex quantum systems. An illustrative example given details a TEBD simulation of a spin-½ Heisenberg chain, showcasing TeNPy's capability to manage substantial lattice systems efficiently. Another example pursues a phase diagram characterization of the 2D Ising model on an infinite cylindrical lattice, demonstrating the library's robust implementation of the DMRG method to capture critical phenomena and symmetry-breaking transitions.

Performance and Benchmarking

TeNPy is benchmarked against other prominent libraries like ITensor, revealing comparable performance, especially when operations scale with the bond dimension χ. The library's efficiency is primarily attributed to its reliance on optimized BLAS/LAPACK libraries for heavy computational lifting, rendering Python's perceived limitations as negligible when executed appropriately. Benchmarks have demonstrated robust scalability across multiple cores, with optimal multi-threading performance achieved at sufficiently large tensor dimensions.

Future Developments

Future enhancements aim to expand TeNPy's capabilities further with support for non-Abelian symmetries, fermionic and anyonic systems, and integration with GPU-accelerated operations. Additionally, potential extensions include more sophisticated quantum circuit simulations and broader classes of tensor networks like PEPS and isoTNS. These advancements will align TeNPy with the cutting-edge needs of quantum theoretical research.

Implications and Prospects

TeNPy is positioned as an essential tool for the computational physics community, enabling detailed exploration of quantum systems with sophisticated tensor network techniques. Its continuous development promises to facilitate breakthroughs in understanding quantum entanglement, phase transitions, and other pivotal phenomena in condensed matter physics. As TeNPy evolves, it will likely spur more comprehensive investigations and enhance the accessibility and accuracy of quantum simulations. The prospective integration with machine learning libraries like PyTorch further underscores TeNPy's role in driving forward multidisciplinary research at the intersection of quantum computing and artificial intelligence.