Quantum States on Harmonic Lattices
- 254 Downloads
We investigate bosonic Gaussian quantum states on an infinite cubic lattice in arbitrary spatial dimensions. We derive general properties of such states as ground states of quadratic Hamiltonians for both critical and non-critical cases. Tight analytic relations between the decay of the interaction and the correlation functions are proven and the dependence of the correlation length on band gap and effective mass is derived. We show that properties of critical ground states depend on the gap of the point-symmetrized rather than on that of the original Hamiltonian. For critical systems with polynomially decaying interactions logarithmic deviations from polynomially decaying correlation functions are found.
KeywordsCorrelation Length Gaussian State Hamiltonian Matrix Polynomial Decay Correlation Decay
Unable to display preview. Download preview PDF.
- 13.Hastings M.B., Koma T. Spectral gap and exponential decay of correlations. http://arxiv.org/list/ math-ph/0507008, 2005Google Scholar
- 15.Auerbach A. (1994) Interacting electrons and quantum magnetism. Springer Verlag, New YorkGoogle Scholar
- 27.Bleistein N., Handelsman R.A. (1986) Asymptotic expansions of integrals. Dover Publication, New YorkGoogle Scholar