Exact Ground States with Deconfined Gapless Excitations for the Three-Leg Spin-1/2Tube

Abstract

We consider a spin-1/2 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-3/2 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.