Preroughening Transitions in Crystal Surfaces
Valence Bond Phases in Quantum Spin Chains

Marcel den Nijs and Koos Rommelse

Department of Physics, University of Washington,
Seattle, Washington 98195-1560

Physical Review B 40, 4709-4734 (1989)


We show that disordered flat phases in crystal surfaces are equivalent to valence bond type phases in integer and half-integer spin quantum chains. In the quantum spin representation the disordered flat phase represents a fluid type phase with long-range antiferromagnetic spin order. This order is stabilized dynamically by the hopping of the particles and short-range spin exchange interactions. The mass of Neel solitons is finite. Numerical finite-size-scaling results confirm this. We identify the order parameter of the valence bond phase. The Haldane conjecture suggests a fundamental difference between half-integer and integer antiferromagnetic Heisenberg spin chains. We find that disordered flat phases are realized in both cases, have exactly the same type of long-range antiferromagnetic spin order, and are stabilized by exactly the same mechanism. They differ only in the mathematical formulation of broken symmetry in the spin representation. We suggest experimental methods of observing disordered flat phases in crystal surfaces.

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