Magnetization in a non-equilibrium quantum spin system

• URL: http://arxiv.org/abs/2406.00268v1
• Date: Sat, 1 Jun 2024 02:16:24 GMT
• Title: Magnetization in a non-equilibrium quantum spin system
• Authors: X. Z. Zhang,
• Abstract summary: We show that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The dynamics described by the non-Hermitian Hamiltonian typically capture the short-term behavior of open quantum systems before quantum jumps occur. In contrast, the long-term dynamics, characterized by the Lindblad master equation (LME), drive the system towards a non-equilibrium steady state (NESS), which is an eigenstate with zero energy of the Liouvillian superoperator, denoted as $\mathcal{L}$. Conventionally, these two types of evolutions exhibit distinct dynamical behaviors. However, in this study, we challenge this common belief and demonstrate that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The criticality of the system arises from the exceptional point (EP) of the effective non-Hermitian Hamiltonian. Additionally, the NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. We apply this finding to a series of critical open quantum systems and show that a local dissipation channel can induce collective alignment of all spins in the same direction. This direction can be well controlled by modulating the quantum jump operator. The corresponding NESS is a product state and maintains long-time coherence, facilitating quantum control in open many-body systems. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.

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