Mixed-State Phase Transitions in Measurement-Dressed Imaginary-Time Evolution
arXiv:2511.04402
The paper introduces measurement-dressed imaginary-time evolution (MDITE), which interleaves imaginary-time filtering with local projective measurements, and studies how this competition induces mixed-state phase transitions and symmetry breaking in quantum spin models.
Abstract
Motivated by the ubiquity of decoherence in quantum hardware and the growing role of imaginary-time evolution (ITE) in quantum algorithms, we investigate how many-body correlations generated by imaginary-time filtering are modified by local decoherence. We introduce measurement-dressed imaginary-time evolution (MDITE), which alternates ITE with projective-measurement channels, producing a competition between low-energy filtering and local dephasing. By developing a new efficient quantum Monte Carlo method, we uncover MDITE mixed-state transitions with spontaneous-symmetry-breaking signatures in the driving of 1D transverse-field Ising and 2D columnar dimerized Heisenberg Hamiltonians in the resulting density matrices. In the continuous limit, the Choi-Jamiolkowski mapping yields a tractable equilibrium description with conformal criticality that qualitatively captures the phase transitions. At finite protocol parameters, however, the four-point correlator violates the conformal cross-ratio form and the critical exponents deviate from their continuous-limit values, signaling the loss of conformal symmetry and richer nonequilibrium criticality. Our results establish MDITE as a controlled setting for exploring mixed-state phases and critical phenomena driven by the interplay between imaginary-time filtering and decoherence.
(14 + 11) pages, 19 figures