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.
Related
- P3MaZe: a Mass-Zero constrained-dynamics formulation of particle-mesh electrostatics
- Geometric formulation of state-dependent Langevin dynamics using scalar free energy
- A reduced formulation for the free-wave propagation analysis in composite structures
- Dynamics of Majorana tetron qubits under quasiparticle poisoning
- A Bonded-Particle Discrete-Element Model with Self-Gravity for the Collision and Reaccumulation of Rubble-Pile Asteroids: Formulation and Numerical Protocol
BibTeX
@misc{wang2026majorana,
title = {{A Majorana Formulation of Time-Dependent Two-Particle Reduced-Density-Matrix Dynamics}},
author = {Haoran Wang and Alessandro Principi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23993},
eprint = {2609.23993},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23993},
}
RIS
TY - UNPB
TI - A Majorana Formulation of Time-Dependent Two-Particle Reduced-Density-Matrix Dynamics
AU - Haoran Wang
AU - Alessandro Principi
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.23993
UR - https://arxiv.org/abs/2609.23993
AB - 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.
ER -