T3NS: three-legged tree tensor network states

TL;DR

The paper introduces T3NS, a novel three-legged tree tensor network state that combines the benefits of DMRG and TTNS, enabling efficient simulation of complex quantum chemical systems.

Contribution

It proposes the T3NS ansatz, integrating physical and branching tensors to improve entanglement handling while maintaining low computational costs.

Findings

Successfully simulated quantum chemical Hamiltonians.

Demonstrated proof-of-principle calculations on LiF, N₂, and copper peroxide isomers.

Abstract

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of-principle calculations on LiF, N$_2$ and the bis($\mu$-oxo) and $\mu - \eta^2 : \eta^2$ peroxo isomers of $[\mathrm{Cu}_2\mathrm{O}_2]^{2+}$.