Spin Liquid and Superconductivity emerging from Steady States and Measurements

Understand

We demonstrate that, starting with a simple fermion wave function, the steady mixed state of the evolution of a class of Lindbladians, and the ensemble created by strong local measurement of fermion density without post-selection can be mapped to the "Gutzwiller projected" wave functions in the doubled Hilbert space -- the representation of the density matrix through the Choi-Jamiolkowski isomorphism.

• A Gutzwiller projection is a broadly used approach of constructing spin liquid states.
• For example, if one starts with a gapless free Dirac fermion pure quantum state, the constructed mixed state corresponds to an algebraic spin liquid in the doubled Hilbert space.
• We also predict that for some initial fermion wave function, the mixed state created following the procedure described above is expected to have a spontaneous "strong-to-weak" U(1) symmetry breaking, which corresponds to the emergence of superconductivity in the doubled Hilbert space.