Emergence of spin-active channels at a quantum Hall interface

We study the ground state of a system with an interface between $\ensuremath{\nu}=4$ and $\ensuremath{\nu}=3$ in the quantum Hall regime. Far from the interface, for a range of interaction strengths, the $\ensuremath{\nu}=3$ region is fully polarized but $\ensuremath{\nu}=4$ region is unpolarized. Upon varying the strength of the interactions and the width of the interface, the system chooses one of two distinct edge/interface phases. In phase $A$, stabilized for wide interfaces, spin is a good quantum number, and there are no gapless long-wavelength spin fluctuations. In phase $B$, stabilized for narrow interfaces, spin symmetry is spontaneously broken at the Hartree-Fock level. Going beyond Hartree-Fock, we argue that phase $B$ is distinguished by the emergence of gapless long-wavelength spin excitations bound to the interface, which can be detected by a measurement of the relaxation time ${T}_{2}$ in nuclear magnetic resonance.