Quantum states on harmonic lattices

Norbert Schuch, J. Ignacio Cirac, Michael M. Wolf

Research output: Contribution to journalArticlepeer-review

52 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)65-92
Number of pages28
JournalCommunications in Mathematical Physics
Volume267
Issue number1
DOIs
StatePublished - Oct 2006
Externally publishedYes

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