Spin models in 1D environments: exact solutions and emergent steady-state order

In this talk, I will discuss spin models for open quantum systems in 1D baths, which, in contrast to the Dicke limit, typically lack total permutational symmetry. First, I will present a symmetry-based method that provides an exponential reduction in the complexity of a broad class of such problems. I will identify conditions under which partial permutational symmetry emerges and exploit it to group qubits into collective multi-level degrees of freedom, which we term superspins [1]. These superspins obey a generalized angular momentum algebra, reducing the relevant Hilbert space dimension from exponential to polynomial, enabling exact many-body simulations of dynamics. Second, I will show that under suitable incoherent pumping, the dynamics of these systems enters a synchronization window in which collective decay overcomes decoherence, leading to spontaneous steady-state phase ordering and superradiant emission [2]. These results clarify how competition and propagation shape emergent order in one-dimensional reservoirs and identify regimes where steady-state superradiance may arise beyond the Dicke limit.



[1] arXiv:2505.00588 (2025)

[2] arXiv:2511.10638 (2025)