Ising chain with topological degeneracy induced by dissipation

Abstract

The ground-state degeneracy of the quantum spin system is a characteristic of nontrivial topology, when it is gapped and robust against disordered perturbation. The corresponding quantum phase transition (QPT) is usually driven by a real parameter. We study a non-Hermitian Ising chain with two transverse fields, one real and another imaginary, based on the exact solution and numerical simulation. We show that topological degeneracy still exists and can be obtained by an imaginary transverse field from a topologically trivial phase of a Hermitian system. The topological degeneracy is robust against the random imaginary field and therefore expected to be immune to disordered dissipation from the spontaneous decay in experiment. The underlying mechanism is the nonlocal symmetry, which emerges only in thermodynamic limit and relates two categories of QPTs in the quantum spin system, rooted from topological order and symmetry breaking, respectively.

arXiv comment7 pages, 2 figures

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• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Quantum phase transition in a non-Hermitian XY spin chain with global complex transverse field
• Many-body phase transitions in a non-Hermitian Ising chain
• Transition from degeneracy to coalescence: theorem and applications
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Topological phase in Kitaev chain with spatially separated pairing processes
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model
• Dynamic crystallization in a quantum Ising chain
• Nonlocal pseudospin dynamics in a quantum Ising chain