The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks

TL;DR

This paper develops a tensor network approach based on the algebraic Bethe ansatz to efficiently simulate the 1D supersymmetric t-J model, enabling the calculation of ground and excited state properties.

Contribution

It introduces a graded tensor network construction derived from the nested algebraic Bethe ansatz for the supersymmetric t-J model, allowing approximate contractions for state analysis.

Findings

Successfully computed observables for lattices up to 18 sites

Demonstrated the effectiveness of the tensor network approach for strongly correlated electrons

Provided a new computational framework for the t-J model

Abstract

We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product State. As a proof of principle, we calculate observables of ground states and excited states of finite lattices up to $18$ lattice sites.