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 $\ensuremath{\beta}$ function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For $d<{d}_{1}$ and for $d>{d}_{2}$ , the $\ensuremath{\beta}$ 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 $\ensuremath{\beta}$ function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.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 $\ensuremath{\beta}$ function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For $d<{d}_{1}$ and for $d>{d}_{2}$, the $\ensuremath{\beta}$ 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 $\ensuremath{\beta}$ function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.

arXiv:1710.08447Physical Review AJul 30, 201820 citations

Pinpointing Feshbach resonances and testing Efimov universalities in K39

Jiří Etrych, Gevorg Martirosyan, Alec Cao +5 more

Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in $^{39}\mathrm{K}$ , as well as six previously unexplored interstate ones. We perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length $a$ and permits precision measurements of the signatures of Efimov physics across four intermediate-strength intrastate resonances. We measure the modulation of the ${a}^{4}$ scaling of the three-body loss coefficient for both $a<0$ and $a>0$ , as well as the many-body loss dynamics at unitarity (where $a$ diverges). The absolute positions of the observed Efimov features confirm a ubiquitous breakdown of Efimov--van der Waals universality in $^{39}\mathrm{K}$ , while their relative positions are in agreement with the universal Efimov ratios. The loss dynamics at unitarity are the same (within experimental uncertainties) for the three broadest Feshbach resonances, consistent with observing little variation in the widths of the corresponding Efimov features.Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in $^{39}\mathrm{K}$, as well as six previously unexplored interstate ones. We perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length $a$ and permits precision measurements of the signatures of Efimov physics across four intermediate-strength intrastate resonances. We measure the modulation of the ${a}^{4}$ scaling of the three-body loss coefficient for both $a<0$ and $a>0$, as well as the many-body loss dynamics at unitarity (where $a$ diverges). The absolute positions of the observed Efimov features confirm a ubiquitous breakdown of Efimov--van der Waals universality in $^{39}\mathrm{K}$, while their relative positions are in agreement with the universal Efimov ratios. The loss dynamics at unitarity are the same (within experimental uncertainties) for the three broadest Feshbach resonances, consistent with observing little variation in the widths of the corresponding Efimov features.

arXiv:2208.13766Physical Review ResearchMar 13, 202331 citations

Efimov physics in a finite volume

Simon Kreuzer, H.‐W. Hammer

arXiv:0811.0159Physics Letters BFeb 27, 200982 citations

Liberating Efimov Physics from Three Dimensions

Yusuke Nishida, Shina Tan

arXiv:1104.2387Few-Body SystemsJul 18, 201150 citations

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 $\ensuremath{\beta}$ function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For

d<{d}_{1}

and for

d>{d}_{2}

, the $\ensuremath{\beta}$ 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 $\ensuremath{\beta}$ function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.

Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in

^{39}\mathrm{K}

, as well as six previously unexplored interstate ones. We perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length

a

and permits precision measurements of the signatures of Efimov physics across four intermediate-strength intrastate resonances. We measure the modulation of the

{a}^{4}

scaling of the three-body loss coefficient for both

a<0

and

a>0

, as well as the many-body loss dynamics at unitarity (where

a

diverges). The absolute positions of the observed Efimov features confirm a ubiquitous breakdown of Efimov--van der Waals universality in

^{39}\mathrm{K}

, while their relative positions are in agreement with the universal Efimov ratios. The loss dynamics at unitarity are the same (within experimental uncertainties) for the three broadest Feshbach resonances, consistent with observing little variation in the widths of the corresponding Efimov features.