2013/11/03 by Eric Duchon, Duchon, Eric, Yen Lee Loh +3 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Gases (cond-mat.quant-gas) #Semiconductor Quantum Structures and Devices
paper · pdf · doi:10.48550/arxiv.1311.0543
openalex publication_date 2013/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This chapter is a pedagogical review of the Hubbard model for bosons with repulsion and for fermions with attraction and repulsion primarily using two methods, one chosen for its simplicity and insights (mean field theory) and the other chosen for its accuracy and reliability (quantum Monte Marlo methods). From a comparison of the two methods we glean valuable information into the effects of fluctuations that dominate quantum phase transitions. The chapter includes an in-depth comparison with experiments. We conclude with a discussion of future developments where the technical methods expounded on here, mean field theory and quantum Monte Carlo, could be useful.