Spectral Gap and Decay of Correlations in U(1)-Symmetric Lattice Systems in Dimensions D<2

Details Spectral Gap and Decay of Correlations in U(1)-Symmetric Lattice Systems in Dimensions D<2 Spectral Gap and Decay of Correlations in U(1)-Symmetric Lattice Systems in Dimensions D<2

2005-05-08

arxiv.org/abs/math-ph/0505022v3

J.Math.Phys.48:023303,2007

Physics

Mathematical Physics

19 pages, no figures, v2: title modified, all the results modified, a result in D=2 added, references added; v3: the result in

Scientific paper

10.1063/1.2437652

We consider many-body systems with a global U(1) symmetry on a class of lattices with the (fractal) dimensions 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 order.

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