Tuning quantum chains with long-range measurement operators

Measurements not only enable passively probing quantum matter, but can also provide an active control knob for inducing novel phenomena.  For instance, recent works have shown that local weak measurements on 1D quantum critical systems can qualitatively alter universal long-distance properties.  General arguments, however, indicate that symmetric local weak measurements preserve the universal structure of 1D gapped phases. We demonstrate that long-range weak measurements can drive transitions in both gapless and gapped 1D systems. As an example, we study transverse-field Ising chains subjected to long-range measurements that promote ferromagnetism.  When the pre-measurement state realizes the gapped disordered phase, measurements induce a transition to a novel long-range-ordered state with power-law disorder parameter correlations. This transition persists even when the initial state sits at the Ising critical point. Our results are supported by RG analyses and Monte Carlo simulations, and establish a loophole for tuning low-dimensional gapped quantum phases through a single round of weak measurement.