Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains

TLDR

In the quantum spin representation, the disordered flat phase is a fluid‑like state with long‑range antiferromagnetic spin order, and the Haldane conjecture highlights a fundamental difference between half‑integer and integer antiferromagnetic Heisenberg spin chains. The study proposes experimental methods to observe disordered flat phases on crystal surfaces. The disordered flat phase is stabilized dynamically by particle hopping and short‑range spin‑exchange interactions. The study demonstrates that disordered flat phases on crystal surfaces correspond to valence‑bond phases in both integer and half‑integer spin chains, with finite Néel soliton mass, a confirmed order parameter, and identical long‑range antiferromagnetic order stabilized by the same mechanism, differing only in the mathematical description of broken symmetry.

Abstract

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 N\'eel 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.