Efficient Tensor Network ansatz for high-dimensional quantum many-body problems

TL;DR

This paper presents a new tensor network structure that efficiently models high-dimensional quantum many-body systems, achieving high precision and scalability, and enabling detailed phase diagram computations for complex quantum models.

Contribution

A novel tensor network structure that maintains area law compliance in high dimensions, improving scalability and precision over existing methods.

Findings

Demonstrated unprecedented accuracy in 2D spin model benchmarks

Successfully computed phase diagrams of 2D Rydberg atom systems

Observed non-trivial quantum phases and phase transitions

Abstract

We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently manipulatable and scalable. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes. Finally, we compute the ground state phase diagram of two-dimensional lattice Rydberg atoms in optical tweezers observing non-trivial phases and quantum phase transitions, providing realistic benchmarks for current and future two-dimensional quantum simulations.