Higgs boson in a 2D superfluid To be, or not to be in d=2 Whats the drama? N. Prokofev ICTP, Trieste, July 18, 2012 WIBG: : collective excitations are overdamped (classical criticality) In a Galilean system phase and density are canonical variables and the spectrum is exhausted by Bogoliubov quasiparticles Strongly interacting superlfuids: At we have and the amplitude mode energy is comparable to overlap with other modes. Suppressing by interactions: is the necessary condition for emergence of the new soft mode (Higgs), but Liquid-Solid first order transition may happen instead Why not to be in a generic superfluid? Bose Hubbard model: Particle-hole symmetric Lorentz-invariant QCP Capogrosso-Sansone, Soyler et al. 08 To be or not to be in d=3,2 ? Asymptotically exact mean-field Higgs mode is well-defined. Overdamped due to strong decay into two Goldstone modes. No Higgs resonance at low energy in any correlation function in close vicinity to the QCP Chubukov, Sachdev, Ye 93 Altman, Auerbach 02 Zwerger 04 Podolsky, Auerbach, Arovas 11 d=3d=2 Does it help to move away from QCP towards Galilean system? [Yes --- mean-field/variational, 1/N, RPA] Huber, Buchler, Theiler, Altman, Blatter 08, 07 Menotti, Trivedi 08 ??? Chubukov, Sachdev, Ye 93 Podolsky, Auerbach, Arovas 11 Look at the right response function! Scalar susceptibility is a better candidate Not to be in d=2: 1/N predictions for scalar susceptibility Altman, Auerbach 02 Polkovnikov, Altman, Demler, Halperin, Lukin 05 Podolsky, Auerbach, Arovas (2011) Peak width INCREASES as Peak maximum > non-universal scale, no Higgs resonance in the relativistic limit. Universal scaling predictions Chubukov, Sachdev, Ye 93 Sachdev 99 A B Podolsky et al. MISSING SPECTRAL DENSITY Scalar response through lattice modulation Linear response for small Energy dissipation rate : Total energy absorbed: : Recent Munich: The onset of quantum critical continuum. Resonance can not be seen due to inhomogeneous broadening. Onset frequency TIME TO CALL WORMS! Quantum Monte Calro: BH model in path integral representation + WA No systematic errors but (ii) finite system size L=20: + explicit checks of no size dependence (i) finite simulation time: for lowest frequencies (ii) imaginary time (Matsubara frequencies) analytic continuation Ill-posed problem: MaxEnt=most likely most featureless space Lattice path-integral = expansion of in hopping transitions, or kinks Kinetic energy = sum of all hopping transitions kink-kink correlation function Results are person, continent, and CPU indendent, and agree with accuracy for the lowest frequencies There is a resonance at low frequency which - emerges at - softens as - gets more narrow as - preserves its amplitude (roughly) Side-by-side comparison Higgs resonance is present only in close vicinity of QCP. Barely seen at U=14, impossible to disentangle from other modes at U=12 Higgs resonance in the MI phase where is the Mexican hat potential? Power-point attempt to compare signals (amplitude adjusted) One (small ?) problem for direct comparison: experiment = Most recent 1/N calculation by Podolsky & Sachdev [arXiv: ]arXiv: Universal part of the scalar response has an oscillating component ! Pade approximants Conclusions: Universal part QMC simulation Higgs resonance Possible to extract experimentally in traps and at finite temperature.