Quantum states on harmonic lattices
type: Item
instance of: scholarly article
title: Quantum states on harmonic lattices
zbMATH Open document ID: 1110.82015
author: Norbert Schuch
author: J. Ignacio Cirac
author: Michael M. Wolf
published in: Communications in Mathematical Physics
publication date: 2007-02-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/quant-ph/0509166
review text: 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.
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B27
zbMATH DE Number: 5125453
zbMATH Keywords: bosonic Gaussian quantum states
zbMATH Keywords: infinite cubic lattice
zbMATH Keywords: quadratic Hamiltonians, critical and noncritical cases
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
OpenAlex ID: W2051928607
arXiv ID: quant-ph/0509166
Wikidata QID: Q59458740
cites work: BCS-like modewise entanglement of fermion Gaussian states
cites work: ENTANGLEMENT AND FRUSTRATION IN ORDERED SYSTEMS
cites work: Lieb-Robinson bounds and the exponential clustering theorem
cites work: Spectral gap and exponential decay of correlations
cites work: On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems
cites work: Quasi-free states of the C.C.R.-algebra and Bogoliubov transformations
cites work: Q5608349
cites work: Bounds for the entries of matrix functions with applications to preconditioning
cites work: Q4092387
DOI: 10.1007/S00220-006-0049-6
description: scientific article