Combined tensor network/cluster expansion method using logic gates: Illustrated for (bi)excitons by a single-layer MoS2 model system

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 the 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., wave functions 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 ${\mathrm{MoS}}₂$-like model system.