PyTreeNet: A Python Library for easy Utilisation of Tree Tensor Networks

TL;DR

PyTreeNet is a Python library that simplifies the implementation and simulation of tree tensor network methods for quantum systems, including time evolution, with practical examples and exercises.

Contribution

It provides a comprehensive, user-friendly Python toolkit for tree tensor network algorithms, focusing on quantum system time evolution, which enhances accessibility and application scope.

Findings

Successfully simulates complex quantum models beyond traditional methods

Includes implementations of tensor decompositions and tree structures

Demonstrates capabilities with a modified Ising model example

Abstract

In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library PyTreeNet. It includes code examples and exercises to introduce the library's functions and familiarise the reader with the concepts and methods surrounding tree tensor networks. PyTreeNet implements all the tools required to implement general tree tensor network methods, such as tensor decompositions and arbitrary tree structures. The main focus is on the time evolution of quantum systems. This includes an introduction to tree tensor network states and operators and the time-evolving block decimation and time-dependent variational principle. The library's capabilities are showcased with the example of a modified transverse field Ising model on tree structures that go far beyond the ability of common state vector methods.