Dilute Fermi and Bose gases

We consider a number of different models in this chapter, but they share some important unifying characteristics. They all have a global U(1) symmetry. We are particularly interested in the behavior of the conserved density, generically denoted as *Q*, associated with this symmetry. All the models exhibit a quantum phase transition between two phases with the a specific *T* = 0 behavior in the expectation value of *Q*. In one of the phases á*Q* ñ is pinned precisely at a quantized value, and does not vary as microscopic parameters are varied. This quantization ends at the quantum critical point with a discontinuity in the derivative of á*Q* ñ with respect to the tuning parameter, and á*Q* ñ varies smoothly in the other phase; there is no discontinuity in the value of á*Q* ñ, however.

We have already met a transition of the above type in the previous Chapter 10: the Mott insulator to superfluid transition. The finite temperature crossovers near this transition are discussed in some detail, including their exact determination in *d* = 1. We also discuss a closely related transition in a dilute Fermi gas: exact crossovers can be determined here in general *d*, and this provides a simple and instructive example of the physics near a quantum critical point.

- Some of the results in Section 11.3 on the dilute Bose gas were also obtained in work that was not cited: E. B. Kolomeisky and J. P. Straley,
*Phys. Rev. B***46**, 11749 (1992) and*Phys. Rev. B***46**, 13942 (1992).

NEXT ; TABLE OF CONTENTS