Functional renormalization for quantum phase transitions with non-relativistic bosons

Abstract

Functional renormalization yields a simple unified description of bosons at zero temperature, in arbitrary space dimension $d$ and for $M$ complex fields. We concentrate on nonrelativistic bosons and an action with a linear time derivative. The ordered phase can be associated with a nonzero density of (quasi) particles $n$. The behavior of observables and correlation functions in the ordered phase depends crucially on the momentum $k_{ph}$, which is characteristic for a given experiment. For the dilute regime $k_{ph}\gtrsim n^{1/d}$ the quantum phase transition is simple, with the same ``mean field'' critical exponents for all $d$ and $M$. On the other hand, the dense regime $k_{ph}\ll n^{1/d}$ reveals a rather rich spectrum of features, depending on $d$ and $M$. In this regime one observes for $d\le 3$ a crossover to a relativistic action with second time derivatives. This admits order for $d>1$, whereas $d=1$ shows a behavior similar to the low temperature phase of the classical two-dimensional $O(2M)$-models.

31 pages, new references

References in corpus (3)

• Flow Equations for the BCS-BEC Crossover
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Functional renormalization group for d-wave superconductivity in Hubbard type models

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• Renormalization group for phases with broken discrete symmetry near quantum critical points
• Nonperturbative thermodynamics of an interacting Bose gas
• Renormalized phi^6 model for quantum phase transitions in systems of itinerant fermions
• Superfluid to Mott-insulator transition of cold atoms in optical lattices
• Occupation numbers from functional integral