Physics – Mathematical Physics
Scientific paper
2005-09-21
Physics
Mathematical Physics
The main result in section 3 was reviewed and a major changes appeared in section 4
Scientific paper
Though our primary motivation is to study properties of the ground states of a Hamiltonian for quantum spin chain, in this exposition we propose a general methodology valid for a translation invariantstate. To that end we study the associated Popescu systems [Po,BJKW] representing the translation invariant state and find an useful criteria for the state to be pure. As a simple consequence of this criteria we prove a surprising result which says that there exists no real lattice symmetric translation invariant and SU(2)-gauge invariant pure state for half-odd integer spin chain. As a consequence of this result we prove that ground state for half-odd integer spin chain is not unique for any SU(2)-gauge invariant Hamiltonian. In other words this exhibits that there is a phase transition in the ground state for anti-ferromagnetic isotropic Heisenberg half-odd integer spin chain.
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