Functional renormalization for quantum phase transitions with non-relativistic bosons

TL;DR

This paper applies functional renormalization to nonrelativistic bosons at zero temperature, revealing different critical behaviors in dilute and dense regimes and a crossover to relativistic dynamics in dense regimes for certain dimensions.

Contribution

It provides a unified functional renormalization framework for nonrelativistic bosons across various dimensions and particle numbers, highlighting regime-dependent behaviors and a crossover to relativistic physics.

Findings

Dilute regime exhibits mean field critical exponents across dimensions.

Dense regime shows a crossover to relativistic action for $d \\leq 3$.

Behavior in $d=1$ resembles classical two-dimensional $O(2M)$ models.

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 $d\leq 3$ 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.