Conformality Lost in Efimov Physics

Abstract

A general mechanism for the loss of conformal invariance is the merger and disappearance of an infrared fixed point and an ultraviolet fixed point of a renormalization group flow. We show explicitly how this mechanism works in the case of identical bosons at unitarity as the spatial dimension $d$ is varied. For $d$ between the critical dimensions $d_1=2.30$ and $d_2=3.76$, there is loss of conformality as evidenced by the Efimov effect in the three-body sector. The beta function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For $d<d_1$ and for $d>d_2$, the beta function has two real roots that correspond to infrared and ultraviolet fixed points. As $d$ approaches $d_1$ from below and as $d$ approaches $d_2$ from above, the fixed points merge and disappear into the complex plane. For $d_1<d<d_2$, the beta function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.

11 pages, 3 figures

References in corpus (5)

• Fermi gas near unitarity around four and two spatial dimensions
• Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
• Efimov effect from functional renormalization
• Efimov effect in $D$ spatial dimensions in $AAB$ systems
• Ground-state energy of the unitary Fermi gas from the epsilon expansion

Cited by in corpus (11)

• Efimov effect in a $D$-dimensional Born-Oppenheimer approach
• D-dimensional three-body bound-state problem with zero range interactions
• The breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition
• Cold atom-dimer reaction rates with ${}^4$He, ${}^{6,7}$Li and ${}^{23}$Na
• Efimov effect at the Kardar-Parisi-Zhang roughening transition
• Second root of dilute Bose-Fermi mixtures
• Dimensional effects in Efimov physics
• Efimov-like physics in fraction-dimensional Bose systems with three-body interaction
• RG Flows and Dynamical Systems
• Emergence of N-body tunable interactions in universal few-atom system
• Reliability of the Born-Oppenheimer approximation in noninteger dimensions