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(8)
Critical Point
Defect Density
Energy Gap
Exact Diagonalization
Excited States
Ground State Energy
Hilbert Space
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Spin1 Kitaev model in one dimension
Spin1 Kitaev model in one dimension,10.1103/PhysRevB.82.195435,Physical Review B,Diptiman Sen,R. Shankar,Deepak Dhar,Kabir Ramola
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Spin1 Kitaev model in one dimension
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Diptiman Sen
,
R. Shankar
,
Deepak Dhar
,
Kabir Ramola
We study a onedimensional 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∑nSnxSn+1y . The cases where S is integer and halfodd 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 groundstate sector, the system can be mapped to a spin1/2 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∑nWn , and show that this has gapless excitations in the range lambda1c<=lambda<=lambda2c . We use the variational wave functions to study how the groundstate energy and the
defect density
vary near the two critical points lambda1c and lambda2c .
Journal:
Physical Review B  PHYS REV B
, vol. 82, 2010
DOI:
10.1103/PhysRevB.82.195435
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