A Majorana Formulation of Time-Dependent Two-Particle Reduced-Density-Matrix Dynamics

Abstract

We introduce a time-dependent two-particle (TP) reduced-density-matrix algorithm for systems of interacting Majorana fermions. We close the BBGKY hierarchy at the two-particle level by reconstructing the three-particle reduced density matrix from lower-order correlations. To stabilize the evolution, we impose a positivity projection on the two-particle density matrix while preserving chosen conserved quantities such as the energy. We benchmark the approach on quenches in the one-dimensional Hubbard model and on flux dynamics in the Kitaev honeycomb model. For the Hubbard quench, TP captures strong-coupling dynamics missed by Hartree--Fock (HF). For the Kitaev quenches, TP accurately reproduces the early-time flux dynamics in several regimes and provides a substantial improvement over HF when two-particle correlations are important. We further show that gauge coherence is essential for flux dynamics. The projection procedure however introduces an effective irreversibility, which affects the long-time dynamics.