Tensor network strategies for calculating biexcitons and trions in monolayer 2D materials beyond the ground state

TL;DR

This paper presents an advanced tensor network method that efficiently computes exciton, trion, and biexciton states across the full Brillouin zone in monolayer 2D materials, surpassing previous approaches in precision and scalability.

Contribution

It introduces detailed implementation strategies and mathematical foundations for tensor network calculations of excited states beyond the ground state in 2D materials.

Findings

Efficient tensor network approach scales logarithmically with grid points.

Achieved high-precision calculations for excitons, trions, and biexcitons in monolayer MoS₂.

Validated strategies for calculating excited bound states and testing common approximations.

Abstract

Recently in [Phys. Rev. B 99, 241301(R) (2019)] tensor networks build upon logical circuits were briefly introduced to retrieve exciton and biexciton states. Compared to a conventional approach the tensor network methods scales logarithmic instead of linear in the grid points of the Brioullin zone and linear instead of exponential in the number of electrons and holes. This enables calculations with higher precision on the full Brioullin zone than previously possible. In this paper extensive details for an efficient implementation and the corresponding mathematical background are presented. In particular this includes applications and results for excitons, trions and biexcitons (for monolayer MoS$_2$ as example), going beyond the initial brief introduction. Furthermore strategies for calculating selective excited bound states and tests of common approximations are discussed making use of the high accuracy full Brioullin zone treatment of the tensor network method.