论文标题
互动引起的动力学$ \ Mathcal {pt} $对称性破坏了耗散费米 - 哈伯德模型
Interaction induced dynamical $\mathcal{PT}$ symmetry breaking in dissipative Fermi-Hubbard models
论文作者
论文摘要
我们研究了一维消散性费米 - 哈伯德模型的动力学特性,这些模型由Lindblad Master方程与具有站点依赖性跳跃运算符的Lindblad Master方程进行了描述。如果我们补偿系统的总体增益项,则具有纯粹损失术语的相应的非热有效的汉密尔顿人具有平等时间($ \ Mathcal {pt} $)对称性。通过求解具有固定耗散的两个位点Lindblad方程,我们发现重新密度矩阵的动力学显示出不稳定性,因为相互作用在阈值上增加,这可以在非炎性有效的汉密尔顿人方案中等效地描述。在多站点系统中也观察到了这种不稳定,并且与$ \ Mathcal {pt} $对称性破裂密切相关,并伴随着有效的汉密尔顿有效的复杂特征值的外观。此外,我们揭示了抗铁磁莫特阶段的动力不稳定性来自$ \ Mathcal {pt} $对称性在非常激发的频段中破坏,尽管在强烈相互作用方面,非 - 富米式哈伯德模型的低能有效模型始终是Hermitian的。我们还提供了观察动态$ \ Mathcal {pt} $对称性破坏时间的定量估计,该时间可以在实验中探测。
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time ($\mathcal{PT}$) symmetry if we compensate the system additionally an overall gain term. By solving the two-site Lindblad equation with fixed dissipation exactly, we find that the dynamics of rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in the scheme of non-Hermitian effective Hamiltonians. This instability is also observed in multi-site systems and closely related to the $\mathcal{PT}$ symmetry breaking accompanied by appearance of complex eigenvalues of the effective Hamiltonian. Moreover, we unveil that the dynamical instability of the anti-ferromagnetic Mott phase comes from the $\mathcal{PT}$ symmetry breaking in highly excited bands, although the low-energy effective model of the non-Hermitian Hubbard model in the strongly interacting regime is always Hermitian. We also provide a quantitative estimation of the time for the observation of dynamical $\mathcal{PT}$ symmetry breaking which could be probed in experiments.