The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered flat (DOF) phase, is formulated in terms of interacting steps. Finite terraces play a crucial role in the formulation. We start by mapping the statistical mechanics of interacting (up and down) steps onto the quantum mechanics of two species of one-dimensional hard-core bosons. The effect of finite terraces translates into a number-nonconserving term in the boson Hamiltonian, which does not allow a description in terms of fermions, but leads to a two-chain spin problem. The Heisenberg spin-1 chain is recovered as a special limiting case. The global phase diagram is rich. We find the DOF phase is stabilized by short-range repulsions of like steps. On-site repulsion of up-down steps is essential in producing a DOF phase, whereas an off-site attraction between them is favorable but not required. Step-step correlation functions and terrace width distributions can be directly calculated with this method.

Interacting hard-core bosons and surface preroughening / Laio, Alessandro; Santoro, Giuseppe Ernesto; Tosatti, Erio. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - 58:19(1998), pp. 13151-13162. [10.1103/PhysRevB.58.13151]

Interacting hard-core bosons and surface preroughening

Laio, Alessandro;Santoro, Giuseppe Ernesto;Tosatti, Erio
1998-01-01

Abstract

The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered flat (DOF) phase, is formulated in terms of interacting steps. Finite terraces play a crucial role in the formulation. We start by mapping the statistical mechanics of interacting (up and down) steps onto the quantum mechanics of two species of one-dimensional hard-core bosons. The effect of finite terraces translates into a number-nonconserving term in the boson Hamiltonian, which does not allow a description in terms of fermions, but leads to a two-chain spin problem. The Heisenberg spin-1 chain is recovered as a special limiting case. The global phase diagram is rich. We find the DOF phase is stabilized by short-range repulsions of like steps. On-site repulsion of up-down steps is essential in producing a DOF phase, whereas an off-site attraction between them is favorable but not required. Step-step correlation functions and terrace width distributions can be directly calculated with this method.
1998
58
19
13151
13162
https://arxiv.org/abs/cond-mat/9809091
Laio, Alessandro; Santoro, Giuseppe Ernesto; Tosatti, Erio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/13634
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