# Spin-S Kitaev model: Classical ground states, order from disorder, and exact correlation functions

Baskaran, G and Sen, Diptiman and Shankar, R (2008) Spin-S Kitaev model: Classical ground states, order from disorder, and exact correlation functions. In: PHYSICAL REVIEW B, 78 (11). 115116-1-115116-8.

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Official URL: http://prb.aps.org/abstract/PRB/v78/i11/e115116

## Abstract

In the first part of this paper, we study the spin-S Kitaev model using spin-wave theory. We discover a remarkable geometry of the minimum-energy surface in the N-spin space. The classical ground states, called Cartesian or CN-ground states, whose number grows exponentially with the number of spins N, form a set of points in the N-spin space. These points are connected by a network of flat valleys in the N-spin space giving rise to a continuous family of classical ground states. Further, the CN-ground states have a correspondence with dimer coverings and with self-avoiding walks on a honeycomb lattice. The zero-point energy of our spin-wave theory picks out a subset from a continuous family of classically degenerate states as the quantum ground states; the number of these states also grows exponentially with N. In the second part, we present some exact results. For arbitrary spin S, we show that localized Z2 flux excitations are present by constructing plaquette operators with eigenvalues ${\pm}1$, which commute with the Hamiltonian. This set of commuting plaquette operators leads to an exact vanishing of the spin-spin correlation functions beyond nearest-neighbor separation found earlier for the spin-1/2 model [G. Baskaran et al., Phys. Rev. Lett. 98, 247201 (2007)]. We introduce a generalized Jordan-Wigner transformation for the case of general spin S and find a complete set of commuting link operators similar to the spin-1/2 model, thereby making the Z2 gauge structure more manifest. The Jordan-Wigner construction also leads, in a natural fashion, to Majorana fermion operators for half-oddinteger spin cases and hard-core boson operators for integer spin cases strongly suggesting the presence of Majorana fermion and boson excitations in the respective low-energy sectors. Finally, we present a modified Kitaev Hamiltonian, which is exactly solvable for all half-odd-integer spins; it is equivalent to an exponentially large number of copies of spin-1/2 Kitaev Hamiltonians.

Item Type: Journal Article Copyright of this article belongs to The American Physical Society. TRANSITIONS; ANYONS; CHAINS Division of Physical & Mathematical Sciences > Centre for High Energy Physics 28 Jan 2010 07:05 19 Sep 2010 04:52 http://eprints.iisc.ernet.in/id/eprint/16468