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DTSTAMP:20260430T135317Z
SUMMARY:Prof Nicolas Dupuis (LPTMC)
DESCRIPTION:Abstract:\nWe discuss the “Higgs” amplitude mode in the rel
 ativistic quantum O($N$) model in two space dimensions. This model describ
 es the critical regime of many condensed-matter systems\, including antife
 rromagnets and the superfluid–Mott-insulator transition of bosons in an 
 optical lattice. We explain why the Higgs resonance does not show up in th
 e longitudinal correlation function but might be observed in the O($N$)-in
 variant scalar susceptibility. After a brief introduction to the nonpertur
 bative renormalization group\, we show how this approach can be used to co
 mpute the scalar susceptibility in the vicinity of the $T=0$ quantum criti
 cal point. In the $T=0$ ordered phase\, we find a well defined Higgs reson
 ance for $N=2$ and $N=3$ and determine its universal properties. The reson
 ance does not exist in the $T=0$ disordered phase but persists at finite t
 emperature. For all values of $N$ larger than 3\, i.e. $Ngeq 4$\, we find 
 that the resonance is suppressed. Our results are compared with quantum Mo
 nte Carlo simulations and $epsilon=4-(d+1)$ expansion about $d=3$.
URL:https://www.imperial.ac.uk/events/104940/prof-nicolas-dupuis-lptmc/
DTSTART;TZID=Europe/London:20150311T140000
DTEND;TZID=Europe/London:20150311T150000
LOCATION:United Kingdom
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