Dissipative spin chains with competing gain and loss exhibit first-order transitions without phase coexistence and mixed-order transitions without U(1) symmetry breaking, driven by PT-symmetry breaking.
To quantify these correlations we calculate ⟨c† a,nca,n+s⟩ = 1 N ∑ k ⟨c† a,kca,k⟩eisk, (A15) which can be evaluated in the same way as the magne- tization above
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Non-equilibrium magnetic phases in spin lattices with gain and loss
Dissipative spin chains with competing gain and loss exhibit first-order transitions without phase coexistence and mixed-order transitions without U(1) symmetry breaking, driven by PT-symmetry breaking.