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Title of Journal: J Low Temp Phys

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Abbravation: Journal of Low Temperature Physics

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Springer US

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DOI

10.1007/s12595-016-0183-x

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1573-7357

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Contact Potential Instability in the PathIntegral

Authors: E Vermeyen J Tempere
Publish Date: 2015/01/13
Volume: 179, Issue: 3-4, Pages: 175-185
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Abstract

It has long been predicted that a twocomponent nonlocalized Fermi gas will exhibit spontaneous polarization for sufficiently strong repulsive interactions a phenomenon which is called itinerant ferromagnetism Recent experiments with ultracold atomic gases have reached the interaction strength for which theoretical models have predicted the occurrence of the normaltoitinerantferromagnetic phase transition but so far this transition has not been observed The instability of the repulsive branch of the Feshbach resonance prevents the formation of the itinerant ferromagnetic state but it is not clear whether this is the only instability impeding its experimental realization In this article we use the pathintegral formalism with density fields in the Hubbard–Stratonovich transformation to study the stability of a homogeneous twocomponent Fermi gas with contact interactions Within the saddlepoint approximation we show that none of the extrema of the action are minima meaning all extrema are unstable to small density fluctuations This implies a more general mechanical instability of the polarized itinerant ferromagnetic and normal states of the system in the pathintegral formalism We find that it is important to consider the stability of the system when studying itinerant ferromagnetism Since mechanical stability may be influenced by the details of the interaction potential we suggest the use of a more realistic potential than the contact potential in future theoretical descriptionsThe authors would like to thank CAR Sá de Melo and A Pelster for useful discussions and JPA Devreese for a careful reading of the manuscript E Vermeyen gratefully acknowledges support in the form of a Ph D fellowship of the Research FoundationFlanders FWO This work was supported by the following Research Programmes of the Research FoundationFlanders FWO G011912N G011512N G018009N and G042915N This work was also supported by the Research Council of Antwerp University via a GOA Grant


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