Particle Statistics, Frustration, and Ground-State Energy

Understand

We study the connections among particle statistics, frustration, and ground-state energy in quantum many-particle systems.

• In the absence of interaction, the influence of particle statistics on the ground-state energy is trivial: the ground-state energy of noninteracting bosons is lower than that of free fermions because of Bose-Einstein condensation and Pauli exclusion principle.
• In the presence of hard-core or other interaction, however, the comparison is not trivial.
• Nevertheless, the ground-state energy of hard-core bosons is proved to be lower than that of spinless fermions, if all the hopping amplitudes are nonnegative.