含时双粒子约化密度矩阵动力学的马约拉纳表述

中文摘要 AI 辅助

我们针对相互作用的马约拉纳费米子系统，提出了一种含时双粒子（TP）约化密度矩阵算法。我们通过从低阶关联重构三粒子约化密度矩阵，在双粒子层面闭合BBGKY层级。为稳定演化，我们在保持能量等选定守恒量的同时，对双粒子密度矩阵施加正定性投影。我们在一维Hubbard模型的淬火动力学和Kitaev蜂窝模型的通量动力学上对该方法进行了基准测试。对于Hubbard淬火，TP方法捕捉到了Hartree-Fock（HF）方法遗漏的强耦合动力学。对于Kitaev淬火，TP方法在多个参数区域准确重现了早期通量动力学，并在双粒子关联重要时相比HF方法提供了显著改进。我们进一步表明，规范相干性对通量动力学至关重要。然而，投影过程引入了有效的不可逆性，这影响了长时间动力学。

英文摘要

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.

发表机构

• University of Manchester（曼彻斯特大学）

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