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arXiv 2607.06293quant-phcond-mat.str-el
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从高斯费米子的非马尔可夫耗散动力学计算强关联基态

Calculating strongly correlated ground states from the non-Markovian dissipative dynamics of Gaussian fermions

Università di Catania(卡塔尼亚大学)

Giuliano Chiriacò

AI总结:

该研究介绍相互作用费米子哈密顿量基态与纯耗散开放量子系统非平衡稳态的映射,通过第三次量子化将费米 - 哈伯德哈密顿量映射到作用于马约拉纳费米子的林德布拉德跃迁算符,虽单个轨迹可高效模拟,但总体计算成本仍高,需进一步研究非马尔可夫解开效率。

摘要:

我们介绍了相互作用费米子哈密顿量的基态与纯耗散开放量子系统的非平衡稳态之间的映射。在第三次量子化框架内,我们将费米 - 哈伯德哈密顿量映射到作用于马约拉纳费米子的林德布拉德跃迁算符上。跳跃项和相互作用项都映射到沿单个量子轨迹保持马约拉纳费米子高斯性的跃迁算符上。动力学可以被解开,每个轨迹仅使用两点关联函数就能有效模拟,计算成本与系统大小呈多项式缩放。我们进一步表明有限粒子数需要负耗散率,导致本质上的非马尔可夫动力学。相应的轨迹解开涉及正负随机权重,表现出符号问题和大波动,收敛需要指数级大量轨迹。尽管单个轨迹有高效的高斯表示,但总体计算成本在系统大小上仍呈指数级,这取决于非马尔可夫解开的计算复杂度,促使对这种解开的效率进行进一步研究。

英文摘要:

We introduce a mapping between the ground state of interacting fermionic Hamiltonians and the non-equilibrium steady state of a purely dissipative open quantum system. Within the framework of third quantization, we map the Fermi-Hubbard Hamiltonian onto Lindblad jump operators acting on Majorana fermions. Remarkably, both hopping and interaction terms map onto jump operators that preserve the Gaussianity of Majorana fermions along individual quantum trajectories. As a result, the dynamics can be unravelled and each trajectory can be simulated efficiently using only two-point correlation functions, with a computational cost that scales polynomially with system size. We further show that finite particle number requires negative dissipative rates, leading to an intrinsically non-Markovian dynamics. The corresponding trajectory unravelling involves both positive and negative stochastic weights and exhibits a sign problem and large fluctuations, so that convergence requires an exponentially large number of trajectories. The overall computational cost remains exponential in system size despite the efficient Gaussian representation of individual trajectories, but is crucially dependent on the computational complexity of the non-Markovian unravelling, motivating further studies on the efficiency of such unravellings.

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