From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz

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.

10 pages, 15 figures

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• A class of quantum many-body states that can be efficiently simulated
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Criticality, the area law, and the computational power of PEPS
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Valence Bond Solids for Quantum Computation
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• TensorNetwork: A Library for Physics and Machine Learning
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Fate of the cluster state on the square lattice in a magnetic field
• Optimization schemes for unitary tensor-network circuit

Cited by in corpus (9)

• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Stabilizer disentangling of conformal field theories
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• Hybrid Tree Tensor Networks for quantum simulation
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Entanglement islands in 1D and 2D lattices with defects