slide1 n.
Skip this Video
Loading SlideShow in 5 Seconds..
Higgs boson in a 2D superfluid PowerPoint Presentation
Download Presentation
Higgs boson in a 2D superfluid

Loading in 2 Seconds...

play fullscreen
1 / 22

Higgs boson in a 2D superfluid - PowerPoint PPT Presentation

  • Uploaded on

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Higgs boson in a 2D superfluid' - nan

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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?


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


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

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


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


Universal scaling predictions

Chubukov, Sachdev, Ye ’93

Sachdev ’99




Podolsky et al.


Scalar response through lattice modulation

Linear response for small

Energy dissipation rate :

Total energy absorbed: :


Recent experiment @ Munich: The onset of quantum critical continuum.

Onset frequency

Resonance can not be seen due to inhomogeneous broadening.


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”


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)


Higgs resonance is present only in close vicinity of QCP.

Barely seen at U=14, impossible to disentangle from other modes at U=12


Power-point attempt to compare signals (amplitude adjusted)

One (small ?) problem for direct comparison: experiment =


Most recent 1/N calculation by Podolsky & Sachdev [arXiv:1205.2700]

Universal part of the scalar response has an oscillating component !

Pade approximants



Higgs resonance

Universal part

QMC simulation

Possible to extract experimentally in traps and at finite temperature.