Ordering controlled by the measurement-feedback interval in quantum Boltzmann samplers

Abstract

We show that the measurement--feedback interval alone can induce ordering in a quantum Boltzmann sampler with fixed programmed couplings and a fixed local dissipative rule. At zero environmental dephasing, repeated projective measurements remove transverse coherence regenerated during relaxation, thereby enhancing the local longitudinal response. We derive the exact finite-interval Markov kernel for successive measurement records and obtain the ordering threshold in the Curie--Weiss limit. For couplings below the equilibrium Curie--Weiss threshold, shortening the readout interval drives a continuous transition to an ordered stationary state even though the programmed Boltzmann distribution remains disordered. The stationary response and equation of state map exactly onto those of a continuously interacting model with dephasing, while the linear relaxation rates remain distinct at matched static response. Exact finite-size stationary calculations reveal the transition through bimodal magnetization distributions and mean-field critical scaling.