Spin-1 Kitaev model in one dimension

Sen, Diptiman ; Shankar, R. ; Dhar, Deepak ; Ramola, Kabir (2010) Spin-1 Kitaev model in one dimension Physical Review B: Condensed Matter and Materials Physics, 82 (19). 195435_1-195435_11. ISSN 1098-0121

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

Related URL: http://dx.doi.org/10.1103/PhysRevB.82.195435


We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S>½ on each site and the Hamiltonian is JΣnSnxSn+1y. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z2-valued conserved quantity Wn 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 dN, where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(√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-½ 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 λΣnWn, and show that this has gapless excitations in the range λ1c≤λ≤λ2c. We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points λ1c and λ2c.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:45526
Deposited On:28 Jun 2011 05:49
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