Measurement-Driven Transitions Between Topological Phases in Spin-1 Chains

We introduce a measurement-only framework for steering spin-1 chains towards competing phases, including symmetry-protected topological phases, trivial phases, and symmetry breaking phases. We start with forced measurements to project the chain to frustrated outcomes, which deterministically drives the system toward one of three archetypal ground states: the symmetry-protected topological, nearest neighbor and next-nearest neighbor AKLT states, a topologically trivial spin-0 state, or a non-SPT spontaneously dimerized VBS state. Using matrix product state simulations, we identify continuous transitions between SPT-SPT, SPT-trivial, and symmetry-broken phases. These transitions are diagnosed using nonlocal string order parameters and entanglement scaling, revealing distinct universality classes with differing critical exponents and a dynamical exponent z≈1 consistent with conformal invariance. Our work establishes measurement-only dynamics as a practical route towards engineering state preparation on near-term quantum devices.