John Hubbard’s challenge 45 years on
12 Jan 2009



Complementarity of condensed matter and cold atom experiments




To explain early inelastic neutron scattering experiments at Harwell, John Hubbard proposed, in 1963, what was to become the standard model of strong correlations. The Hubbard model captures the essence of quantum systems that simultaneously show aspects of itinerancy and localisation. A wealth of experimental information has been obtained since, but exact theoretical or computational predictions are sparse. This limits our ability to verify, or refute, various theoretical scenarios – e.g. postulated soft quantum matter phases intervening between the quantum fluid and crystalline states. Now, novel ultra-cold atom technologies offer the prospect of quantum analogue simulations. We designed a protocol for unbiased determination of the Hubbard model phase diagram. We simulated its performance in one dimension, where exact results are available, finding <3% error. We also showed how to realise experimentally a simpler model displaying soft quantum matter phases. Our theoretical work illustrates how such experiments can be an additional probe of strong correlations, complementary to neutron scattering and other condensed-matter techniques.

J Quintanilla (ISIS), C Hooley (University of St Andrews), ST Carr (University of Birmingham), JJ Betouras (University of St Andrews), VL Campo Jr (Federal University of Sao Carlos), K Capelle (University of Sao Paulo)

Contact:  Dr J Quintanilla,

Research date: December 2008

Further Information

VL Campo et al., Phys. Rev. Lett. 99 (2007) 240403 and J Quintanilla et al., Phys. Rev. A 79 (2009) 031601(R).