Combined tensor network/cluster expansion method using logic gates: Illustrated for (bi-)excitons by a single layer MoS$_2$ model system

TL;DR

This paper introduces a novel tensor network approach using logic gates to efficiently model electron-hole complexes like excitons and biexcitons in 2D materials, demonstrated on a MoS2 model system.

Contribution

It presents a new tensor network method based on logic gates for treating high-dimensional electron-hole states in semiconductors.

Findings

Efficient representation of exciton and biexciton states.

Application to a MoS2 model system.

Potential for improved accuracy in many-body calculations.

Abstract

Carriers such as electrons and holes inside the Brillouin zone of complex semiconducting materials can form bound states (excitons, biexcitons etc.). For obtaining the corresponding eigenstates (e.g. through Wannier or Bethe Salpeter equation) and dynamics (e.g. cluster expansion) the number of involved electrons and holes as well as the accuracy is limited by the appearing high dimensional tensors (i.e. wavefunctions or correlations). These tensors can be efficiently represented and manipulated via tensor network methods. We show how tensor networks formulated via classic logic gates can be used to treat electron-hole complexes inside the Brillouin zone. The method is illustrated for the exciton and biexciton states of a single layer transition metal dichalcogenide MoS$_2$ like model system.