Quantum states on harmonic lattices
The authors investigate bosonic Gaussian quantum states on an infinite cubic lattice in arbitrary spatial dimensions and derive general properties of ground states of translationally invariant quadratic Hamiltonians on such lattice. The obtained results on the asymptotic scaling of ground states correlations both for critical and noncritical cases are summarized in the form of the table in the introduction. They give analytic relations between the decay of the interaction and the correlation functions together with the dependence of the correlation length on band gap and effective mass. For critical systems with polynomially decaying interactions logarithmic derivations from polynomially correlation functions are found.
quadratic Hamiltonians, critical and noncritical cases
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