Strongly-correlated wavefunctions emerging from steady-states and measurements

We demonstrate that the ensemble of states created by strong local measurements of a simple fermionic wavefunction can be mapped to "Gutzwiller projected" wavefunctions in a doubled Hilbert space. These doubled-space wavefunctions are vectorized representations of the density matrix, and their properties may be diagnosed using so-called "Renyi-2" correlation functions. We use this procedure to construct a range of strongly-correlated wavefunctions, including those corresponding to quantum spin liquid states and superconductors. Superconductivity in this doubled-space picture corresponds to strong-to-weak spontaneous symmetry-breaking of the density matrix. We propose "quantum-classical" correlation functions that can be used to characterize these states using real-space "snapshot" measurements. The experimental test of our protocol is in progress.