We study spectral and steady-state properties of generic Markovian dissipative systems described by quadratic fermionic Liouvillian operators of the Lindblad form. The Hamiltonian dynamics is modeled by a generic random quadratic operator, i.e., as a featureless superconductor of class D, whereas the Markovian dissipation is described by $M$ random linear jump operators. By varying the dissipation strength and the ratio of dissipative channels per fermion, $m=M/(2N_F)$, we find two distinct phases where the support of the single-particle spectrum has one or two connected components. In the strongly dissipative regime, this transition occurs for $m=1/2$ and is concomitant with a qualitative change in both the steady-state and the spectral gap that rules the large-time dynamics. Above this threshold, the spectral gap and the steady-state purity qualitatively agree with the fully generic (i.e., non-quadratic) case studied recently. Below $m=1/2$, the spectral gap closes in the thermodynamic limit and the steady-state decouples into an ergodic and a nonergodic sector yielding a non-monotonic steady-state purity as a function of the dissipation strength. Our results show that some of the universal features previously observed for fully random Liouvillians are generic for a sufficiently large number of jump operators. On the other hand, if the number of dissipation channels is decreased the system can exhibit nonergodic features, rendering it possible to suppress dissipation in protected subspaces even in the presence of strong system-environment coupling.
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- 1 Universidade de Lisboa / University of Lisbon
- 2 北京计算科学研究中心 / Beijing Computational Science Research Center [CSRC]
- 3 LPTM / Laboratoire de Physique Théorique et Modélisation
- 4 Univerza v Ljubljani / University of Ljubljana [UL]
- Agence Nationale de la Recherche [ANR]
- European Research Council [ERC]
- Fundação para a Ciência e a Tecnologia (through Organization: Fundação para a Ciência e Tecnologia [FCT])
- Horizon 2020 (through Organization: European Commission [EC])
- Javna Agencija za Raziskovalno Dejavnost RS / Slovenian Research Agency [ARRS]