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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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slide1

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

slide2

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

slide3

Bose Hubbard model:

Particle-hole symmetric

Lorentz-invariant QCP

Capogrosso-Sansone, Soyler et al. ‘08

slide4

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

slide5

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

slide6

Universal scaling predictions

Chubukov, Sachdev, Ye ’93

Sachdev ’99

B

A

MISSING SPECTRAL DENSITY

Podolsky et al.

slide7

Scalar response through lattice modulation

Linear response for small

Energy dissipation rate :

Total energy absorbed: :

slide8

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

Onset frequency

Resonance can not be seen due to inhomogeneous broadening.

slide10

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”

slide11

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

slide12

There is a resonance at

low frequency which

- emerges at

- softens as

- gets more narrow as

- preserves its amplitude (roughly)

slide14

Higgs resonance is present only in close vicinity of QCP.

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

slide19

Power-point attempt to compare signals (amplitude adjusted)

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

slide20

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

Universal part of the scalar response has an oscillating component !

Pade approximants

slide21

Conclusions:

Higgs resonance

Universal part

QMC simulation

Possible to extract experimentally in traps and at finite temperature.