Exact Magnetic Confinement of a Doped Hole by Kinetic Frustration
We establish an exact mechanism of magnetic confinement driven purely by kinetic frustration. In a finite open sawtooth $U=\infty$ Hubbard chain of $L$ unit cells doped with one hole, the ground state at magnetization $M$ contains $M$ polarized triplet dimers surrounding a connected singlet region of length $\ell_{\rm s}=L-M$. A magnetic field selects $M$ and hence the confinement length. The hole forms a standing wave in the singlet region with exponential tails in the triplet background. Confinement requires neither disorder nor an exchange-generated string tension: destructive interference between direct and apex-mediated hopping makes the triplet bonds reflecting. At $t_2/t_1=[2+4\cos(π/(\ell_{\rm s}+2))]^{-1/2}$, they become perfectly reflecting, producing a position-degenerate compact localized state. At every fixed field $0<h<h_{\rm sat}$, the singlet region remains finite as $L\to\infty$ and shrinks stepwise with increasing field, whereas at $h=0$ it spans the system.