Emergent Gauge Fields and the "Choi-Spin Liquids" in Steady States

We demonstrate that the steady states of the evolution of a class of Lindbladians can be mapped to the "Gutzwiller projected" wave functions in the doubled Hilbert space, i.e. the representation of the density matrix through the Choi-Jamiolkowski isomorphism. A Gutzwiller projection is a standard approach of constructing spin liquid states. For example, if one starts with a gapless free fermion pure quantum state, the steady state of the Lindbladian evolution in the doubled Hilbert space is an analog of an algebraic spin liquid, which is dubbed the "Choi-spin liquid". The Choi-spin liquid can also be produced through strong measurement without post-selection. Predictions of the Choi-spin liquids can be made based on the understanding on spin liquids, and we will design the experimental protocol to test these predictions. If one starts with a Chern insulator, theory predicts that the steady state of the Lindbladian evolution is expected to have a spontaneous "strong-to-weak" U(1) symmetry breaking, which corresponds to a superconductor in the doubled Hilbert space.