Disordered flat phase in a solid-on-solid model of fcc(110) surfaces and dimer states in quantum spin-1/2 chains

We present a restricted solid-on-solid Hamiltonian for fcc(110) surfaces. It is the simplest generalization of the exactly solvable body-centered solid-on-solid model which is able to describe a (2 X 1) missing-row reconstructed surface. We study this model by mapping it onto a quantum spin-1/2 chain of the Heisenberg type, with second and third neighbor S(i)(z)S(j)z couplings. The ground-state phase diagram of the spin-chain model is studied by exact diagonalization of finite chains up to N = 28 sites, as well as through analytical techniques. We find four phases in the phase diagram: two ordered phases in which the spins have a Neel type of long-range order (an unreconstructed and a missing-row reconstructed phase, in the surface language), a spin-liquid phase (representing a rough surface), and an intermediate dimer phase which breaks translational invariance and has a doubly degenerate ground state, corresponding to a disordered flat surface. The transition from the (2 x 1) reconstructed phase to the disordered flat phase belongs to the two-dimensional Ising universality class. A critical (preroughening) line with varying exponents separates the unreconstructed phase from the disordered flat phase. The possible experimental signatures of the disordered flat phase are discussed.