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

TL;DR

This paper introduces TeNPy, a Python library for efficient tensor network simulations of quantum many-body systems, focusing on MPS methods like TEBD and DMRG, with practical implementation guidance.

Contribution

It combines a review of tensor product state concepts with the development of a versatile Python library, enabling efficient simulation and symmetry implementation.

Findings

TeNPy facilitates efficient MPS simulations in Python.

Implementation of abelian symmetries accelerates tensor computations.

Practical examples demonstrate the library's capabilities.

Abstract

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) [https://github.com/tenpy/tenpy]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.