Unitary fermions and Lüscher’s formula on a crystal

Manuel Valiente Cifuentes, Nikolaj Thomas Zinner

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
26 Downloads (Pure)


We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the naïve continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak, intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.

Original languageEnglish
Article number114211
JournalScience China: Physics, Mechanics and Astronomy
Issue number11
Early online date18 Sep 2016
Publication statusPublished - Nov 2016


  • effective field theory
  • finite-size effects
  • lattice fermions
  • scattering theory

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Unitary fermions and Lüscher’s formula on a crystal'. Together they form a unique fingerprint.

Cite this