On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains

Details On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains

2008-08-11

arxiv.org/abs/0808.1537v1

Physics

Mathematical Physics

26pages, no figure

Scientific paper

We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As a corollary, we show that gapless excitation exists for spinless Fermion if the pure gauge invariant ground state is non-trivial and translationally invariant.

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