From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz

TL;DR

This paper introduces the Fully-Augmented Tree Tensor Network (FATTN), a new tensor network that enhances entanglement encoding while maintaining computational efficiency, demonstrated through improved ground state energy calculations for the transverse Ising model.

Contribution

The paper proposes FATTN, a novel tensor network that surpasses previous models in entanglement capacity without increasing computational complexity, bridging TTN and MERA.

Findings

FATTN provides more entanglement than TTN and ATTN.

FATTN achieves better accuracy in ground state energy calculations.

FATTN maintains the same computational scaling as TTN and ATTN.

Abstract

Tensor Network States (TNS) offer an efficient representation for the ground state of quantum many body systems and play an important role in the simulations of them. Numerous TNS are proposed in the past few decades. However, due to the high cost of TNS for two-dimensional systems, a balance between the encoded entanglement and computational complexity of TNS is yet to be reached. In this work we introduce a new Tree Tensor Network (TTN) based TNS dubbed as Fully- Augmented Tree Tensor Network (FATTN) by releasing the constraint in Augmented Tree Tensor Network (ATTN). When disentanglers are augmented in the physical layer of TTN, FATTN can provide more entanglement than TTN and ATTN. At the same time, FATTN maintains the scaling of computational cost with bond dimension in TTN and ATTN. Benchmark results on the ground state energy for the transverse Ising model are provided to demonstrate the improvement of accuracy of FATTN over TTN and ATTN. Moreover, FATTN is quite flexible which can be constructed as an interpolation between Tree Tensor Network and Multiscale Entanglement Renormalization Ansatz (MERA) to reach a balance between the encoded entanglement and the computational cost.