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Spin-1 Kitaev model in one dimension

Sen, Diptiman and Shankar, R and Dhar, Deepak and Ramola, Kabir (2010) Spin-1 Kitaev model in one dimension. In: Physical Review B: Condensed Matter and Materials Physics, 82 (19).

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Official URL: http://prb.aps.org/abstract/PRB/v82/i19/e195435

Abstract

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

Item Type: Journal Article
Additional Information: Copyright of this article belongs to The American Physical Society.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 21 Dec 2010 09:29
Last Modified: 21 Dec 2010 09:29
URI: http://eprints.iisc.ernet.in/id/eprint/34552

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