Authors Referees APS Members |
November 2007, to be published in Physical Review B1
Highest weight state description of the isotropic spin-$1$ chain
We introduce an overcomplete highest weight state basis as a calculational tool for the description of the isotropic spin-$1$ chain with bilinear exchange coupling $J_1$ and biquadratic coupling $J_2$. The ground state can be expressed exactly at the three special points in the phase diagram where the Hamiltonian corresponds to a sum of nearest neighbor total spin projection operators ($J_1=0>J_2$, $J_1=-J_2<0$, and $J_1=-J_2/3>0$). In particular, at the phase transition point $J_1=-J_2<0$ it is possible to exactly compute the ground states, excited states, expectation values, and correlation functions by using the new total spin basis. © 2008 The American Physical Society.
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