Universal upper bounds on the Bose-Einstein condensate and the Hubbard star

Universal upper bounds on the Bose-Einstein condensate and the Hubbard star For N hard-core bosons on an arbitrary lattice with d sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by Nmax=(N/d)(d−N+1). This bound can only be attained for one-particle states |φ⟩ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding N-particle state |Ψ⟩ is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state |Ψ⟩ is related to the ground state of a bosonic “Hubbard star” showing Bose-Einstein condensation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Universal upper bounds on the Bose-Einstein condensate and the Hubbard star

Preview Only

Universal upper bounds on the Bose-Einstein condensate and the Hubbard star

Abstract

For N hard-core bosons on an arbitrary lattice with d sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by Nmax=(N/d)(d−N+1). This bound can only be attained for one-particle states |φ⟩ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding N-particle state |Ψ⟩ is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state |Ψ⟩ is related to the ground state of a bosonic “Hubbard star” showing Bose-Einstein condensation.
Loading next page...
 
/lp/aps_physical/universal-upper-bounds-on-the-bose-einstein-condensate-and-the-hubbard-3SOCMa2N97
Publisher
American Physical Society (APS)
Copyright
Copyright © ©2017 American Physical Society
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.064502
Publisher site
See Article on Publisher Site

Abstract

For N hard-core bosons on an arbitrary lattice with d sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by Nmax=(N/d)(d−N+1). This bound can only be attained for one-particle states |φ⟩ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding N-particle state |Ψ⟩ is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state |Ψ⟩ is related to the ground state of a bosonic “Hubbard star” showing Bose-Einstein condensation.

Journal

Physical Review BAmerican Physical Society (APS)

Published: Aug 2, 2017

There are no references for this article.

Sorry, we don’t have permission to share this article on DeepDyve,
but here are related articles that you can start reading right now:

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off