Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems

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 nontrivial phases and quantum phase transitions, providing realistic benchmarks for current and future two-dimensional quantum simulations.

Automated summary

We present a novel tensor network structure to enhance the representation of a quantum many-body wave function, which satisfies the area law in high dimensions and remains efficiently manipulatable. By benchmarking against two-dimensional spin models, we demonstrate unprecedented precision and scalability. Furthermore, we compute the ground state phase diagram of two-dimensional lattice Rydberg atoms, observing nontrivial phases and quantum phase transitions for realistic benchmarks in current and future two-dimensional quantum simulations.