The following hamiltonian is $\mathcal{PT}$-symmetric $$\mathcal{H} = -J \sum_{j = 1}^{2N} [ 1 + (-1)^j \delta ] [ c^{\dagger}_{j} c_{j+1} + h.c. ] + \imath \gamma \sum_{j = 1}^{2N} (-1)^j c^{\dagger}_j c_{j}$$ and it shows real spectra for $\gamma \leq 2J\delta$ (see PhysRevA.86.042110). But this Hamiltonian is non-interacting. Is there any well-known $\mathcal{PT}$-symmetric interacting model?
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$\begingroup$ Link to abstract page? $\endgroup$– Qmechanic ♦Commented Oct 14, 2023 at 2:30
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Yes! There are a few Many-body Hamiltonians given in Ref. PhysRevResearch.2.023286 & PhysRevB.97.201411.
answered Oct 19, 2023 at 10:12