Emergent symmetry-protected topological phases via Polyakov confinement in quantum spin systems.

A main theme in modern condensed matter physics is the emergence of fractionalized excitations and gauge structures from quantum spin systems. However, understanding how these exotic degrees of freedom reconfine into new phases of matter remains a fundamental challenge. In this work, we demonstrate that Polyakov's confinement mechanism-a foundation of compact gauge theory-can serve as a dynamical engine to transform a Dirac spin liquid (DSL) into a symmetry-protected topological (SPT) state. Starting with a DSL with spin-dependent gauge fluxes, we show that the single-occupancy constraint inherent to the physical Hilbert space triggers monopole condensation, dynamically confining bulk spinons while preserving gapless edge modes-realizing a spinon analog of the quantum spin Hall effect. Using a large-scale variational Monte Carlo simulation on a triangular antiferromagnet with an additional Dzyaloshinskii-Moriya interaction, we provide microscopic evidence for this confined SPT phase, including a characteristic area law for the Wilson loop and vanishing topological entanglement entropy. Furthermore, we identify a measurable spin-pump response under magnetic fields, which directly encodes the Berry curvature of the parent Dirac cones. Our results reveal a previously unexplored pathway to SPT physics, bridging the fields of gauge theory, quantum magnetism, and topological matter.