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Optical Lattice Emulators: Bose and Fermi Hubbard Models
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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.
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Shiba duality and $\eta$-altermagnetism: Pairing and charge orders in bipartite attractive Hubbard models
Shiba-dual attractive Hubbard models on bipartite lattices host η-altermagnetism, where Bogoliubov bands split by η-pseudospin with p-, d-, and f-wave structures.
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