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Higgs boson in a 2D superfluid

Higgs boson in a 2D superfluid. N. Prokof’ev. What’s the drama?. To be, or not to be in d=2. ICTP, Trieste, July 18, 2012. Why not to be in a generic superfluid?. WIBG:. In a Galilean system phase and density are canonical variables and the spectrum

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Higgs boson in a 2D superfluid

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  1. Higgs boson in a 2D superfluid N. Prokof’ev What’s the drama? To be, or not to be in d=2 ICTP, Trieste, July 18, 2012

  2. Why not to be in a generic superfluid? WIBG: In a Galilean system phase and density are canonical variables and the spectrum is exhausted by Bogoliubov quasiparticles : collective excitations are overdamped (classical criticality) 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

  3. Bose Hubbard model: Particle-hole symmetric Lorentz-invariant QCP Capogrosso-Sansone, Soyler et al. ‘08

  4. To be or not to be in d=3,2 ? d=3 d=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 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 Look at the right response function! Scalar susceptibility is a better candidate Chubukov, Sachdev, Ye ’93 Podolsky, Auerbach, Arovas ’11

  5. Not to be in d=2: 1/N predictions for scalar susceptibility Podolsky, Auerbach, Arovas (2011) Altman, Auerbach ’02 Polkovnikov, Altman, Demler, Halperin, Lukin ‘05 Peak maximum > non-universal scale , no Higgs resonance in the relativistic limit. Peak width INCREASES as

  6. Universal scaling predictions Chubukov, Sachdev, Ye ’93 Sachdev ’99 B A MISSING SPECTRAL DENSITY Podolsky et al.

  7. Scalar response through lattice modulation Linear response for small Energy dissipation rate : Total energy absorbed: :

  8. Recent experiment @ Munich: The onset of quantum critical continuum. Onset frequency Resonance can not be seen due to inhomogeneous broadening.

  9. TIME TO CALL WORMS!

  10. 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” “< all good fits >” “most featureless”

  11. Lattice path-integral = expansion of in hopping transitions, or kinks Kinetic energy = sum of all hopping transitions space kink-kink correlation function Results are person, continent, and CPU indendent, and agree with accuracy for the lowest frequencies

  12. There is a resonance at low frequency which - emerges at - softens as - gets more narrow as - preserves its amplitude (roughly)

  13. Side-by-side comparison

  14. Higgs resonance is present only in close vicinity of QCP. Barely seen at U=14, impossible to disentangle from other modes at U=12

  15. Higgs resonance in the MI phase – where is the Mexican hat potential?

  16. Power-point attempt to compare signals (amplitude adjusted) One (small ?) problem for direct comparison: experiment =

  17. Most recent 1/N calculation by Podolsky & Sachdev [arXiv:1205.2700] Universal part of the scalar response has an oscillating component ! Pade approximants

  18. Conclusions: Higgs resonance Universal part QMC simulation Possible to extract experimentally in traps and at finite temperature.

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