Spin Liquid and Superconductivity emerging from Steady States and Measurements

TL;DR

This paper shows how certain mixed states of fermions, generated via Lindbladian evolution or measurements, can be mapped to spin liquid and superconducting states using Gutzwiller projections, with implications for experimental realization.

Contribution

It introduces a method to represent mixed fermionic states as Gutzwiller projected wave functions in a doubled Hilbert space, linking measurement-induced states to spin liquids and superconductivity.

Findings

Mixed states can be mapped to Gutzwiller projected wave functions.

Predicted emergence of superconductivity from certain initial states.

Designed experimental protocols for realizing these states.

Abstract

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. We also design the experimental protocol to construct the desired physics of mixed states.