Spectral gap and decay of correlations in U(1)-symmetric lattice systems in dimensions D<2
2007; American Institute of Physics; Volume: 48; Issue: 2 Linguagem: Inglês
10.1063/1.2437652
ISSN1527-2427
Autores Tópico(s)Quantum many-body systems
ResumoWe consider many-body systems with a global U(1) symmetry on a class of lattices with the (fractal) dimension D<2 and their zero temperature correlations whose observables behave as a vector under the U(1) rotation. For a wide class of the models, we prove that if there exists a spectral gap above the ground state, then the correlation functions have a stretched exponentially decaying upper bound. This is an extension of the McBryan-Spencer method at finite temperatures to zero temperature. The class includes quantum spin and electron models on the lattices, and our method also allows finite or infinite (quasi)degeneracy of the ground state. The resulting bounds rule out the possibility of the corresponding magnetic and electric long-range orders.
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