The discussion centers on the negative kinetic energy term in the Bose-Hubbard model, specifically regarding the hopping term, denoted as ##t##. The negative sign in the kinetic term arises from the attractive interaction between particles and lattice sites, leading to negative energy bound states. The hopping parameter ##t## is crucial, as it is typically assumed to be positive (##t>0##), but this may vary depending on the specific system being analyzed. Understanding these dynamics is essential for interpreting the energy spectrum in quantum systems.
PREREQUISITESPhysicists, quantum mechanics students, and researchers focusing on condensed matter physics and quantum lattice models will benefit from this discussion.
Questionasker said:Too familiar with Bose Hubbard model, but suddenly got stuck by a simple question: Why is the kinetic term (to be precise should be single body part) negative?
fzero said:The hopping term is not just the kinetic energy, but also includes the interaction of the particles with the lattice. If the interaction between the particles and the lattice sites is attractive, then often the energy spectrum will contain negative energy bound states (ignoring the other interactions, these are just the analogue of electrons being bound in atoms). Note that the hopping parameter (usually called ##t##) must still be specified. The - sign is usually chosen in the expectation that ##t>0##, but for a specific system, it might not be so.