Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry

Abstract

We systematically study the non-Hermitian version of the one-dimensional anisotropic XY model, which in its original form, is a unique exactly solvable quantum spin model for understanding the quantum phase transition. The distinguishing features of this model are that it has full real spectrum if all the eigenvectors are intrinsic rotation-time reversal (RT) symmetric rather than parity-time reversal (PT) symmetric, and that its Hermitian counterpart is shown approximately to be an experimentally accessible system, an isotropic XY spin chain with nearest neighbor coupling. Based on the exact solution, exceptional points which separated the unbroken and broken symmetry regions are obtained and lie on a hyperbola in the thermodynamic limit. It provides a nice paradigm to elucidate the complex quantum mechanics theory for a quantum spin system.

7 pages, 3 figures

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• Quantum battery with non-Hermitian charging
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• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Topological phase in Kitaev chain with spatially separated pairing processes
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Recognizing critical lines via entanglement in non-Hermitian systems
• Ring-Frustrated Non-Hermitian $XY$ Model
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• Entanglement between uncoupled modes with time-dependent complex frequencies
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• Fermionic model with a non-Hermitian Hamiltonian
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
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• Probing phase transitions in non-Hermitian systems with quantum entanglement