Trap-size scaling in confined particle systems at quantum transitions

Understand

We develop a trap-size scaling theory for trapped particle systems at quantum transitions.

• As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation.
• We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model.
• We present exact and accurate numerical results for the XY chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model.