Abstract
We consider a spin- tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators—one on the triangles and the other on the square plaquettes on the side of the tube—that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i) for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii) for ferromagnetic exchange on the triangles, we recover the phase of the spin- Heisenberg chain; (iii) between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.
- Received 21 July 2011
DOI:https://doi.org/10.1103/PhysRevLett.108.017205
© 2012 American Physical Society