universality and dynamic localization in kibble- zurek

UNIVERSALITY AND DYNAMIC LOCALIZATION IN KIBBLE-ZUREKMichael Kolodrubetz

Boston University

In collaboration with: B.K. Clark, D. Huse (Princeton)A. Polkovnikov, A. Katz (BU)

KIBBLE-ZUREK SCALING

Disordered Ordered


Ramp rate

Kibble-ZurekRamp through the critical

point at a constant, finite rate


Ramp rate


Ramp rate

Fall out ofequilibrium


Ramp rate

Slower


Recent work: Kibble-Zurek rampsshow non-equilibrium scaling (in the limit of slow ramps)

[Chandran et. al., Deng et. al., etc.]


Recent work: Kibble-Zurek rampsshow non-equilibrium scaling (in the limit of slow ramps) More predictions than just defect production!

[Chandran et. al., Deng et. al., etc.]


Excess heat


SchrödingerEquation

ORObservable



ORObservable

Fixed



ORObservable

Fixed

Universaldynamics!=

TRANSVERSE-FIELD ISING CHAIN


Paramagnet (PM) Ferromagnet (FM)


Ramp rate

Slower


Excess heat


Dynamics does not depend on ramp

rate!

OUTLINE

Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives

non-equilibrium critical scaling theory

Part II: Kibble-Zurek with a dynamic field

OUTLINE


non-equilibrium critical scaling theory Are the results universal?


UNIVERSALITY

TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)

UNIVERSALITY

or


UNIVERSALITY

or

Ramp the tilt linearly in time


UNIVERSALITY

or

Ramp the tilt linearly in time: Solve numerically

with DMRG


UNIVERSALITY

UNIVERSALITY

Dynamics are

universal!

OUTLINE


non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs


OUTLINE


non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Non-trivial scaling functions


NON-EQUILIBRIUM PROPERTIES

Spin-spin correlation function


Thermal


Kibble-Z

urek

Thermal


Kibble-Z

urek

Thermal

Antiferromagnetic


Antiferromagnetic

OUTLINE


non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal


OUTLINE


non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal Finite size scaling, dephasing, experiments…


OUTLINE


non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal Finite size scaling, dephasing, experiments…

Part II: Kibble-Zurek with a dynamic field Motivating example: 4 theory

DYNAMIC-FIELD KIBBLE-ZUREK


“Inflaton”

“Higgs field”


When does field get trapped?


Mass density


Mass density

Trapped


Mass density

Ising:

Higgs:

Trapped


Dynamics dominated by critical behavior

DYNAMIC-FIELD KIBBLE-ZUREKF

luct

ua

tion

s a

rou

nd

QC

P

OUTLINE


non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling

functions? Finite size scaling, dephasing, experiments…

Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption

OUTLINE





Should work equally well for Higgs, etc.

OUTLINE





Should work equally well for Higgs, etc. Do dynamics show scaling collapse?

OUTLINE





Should work equally well for Higgs, etc. Do dynamics show scaling collapse?

Expect scaling for


Scaling hypothesisInitial momentum is the

relevant scale for dynamics

OUTLINE




Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse

OUTLINE




Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Effect of ground state potential?

OUTLINE




Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Effect of ground state potential

Is RG relevant

OUTLINE




Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Effect of ground state potential

Is RG relevant Trapping in certain regimes

OUTLINE


non-equilibrium critical scaling theory Are the results universal? What are some properties of the scaling functions? Finite size scaling, dephasing, experiments…

Part II: Kibble-Zurek with a dynamic field System is trapped at QCP by critical absorption Trapping dynamics show scaling collapse Trapping can occur with ground state potential In progress: scaling with potential, emergent

mass, 4 theory, inflationary models…

SUMMARY

Part I: Universality of Kibble-Zurek scaling



phase

EQUILIBRIUM SCALING

“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied

EQUILIBRIUM SCALING

Low energy, long wavelength theory?


EQUILIBRIUM SCALING

Low energy, long wavelength theory



Low energy, long wavelength theory?


Low energy, long wavelength theory


Inverted

DYNAMIC-FIELD ISING CHAIN

Basic idea: Add (classical) dynamics to the transverse field



“Friction” = back-action of spins on field



“Friction” = back-action of spins on field Mass is extensive ( ) Mean-field coupling between field and spins



“Friction” = back-action of spins on field Mass is extensive ( ) Mean-field coupling between field and spins

What happens when field tries to

pass through the critical point?

universality and dynamic localization in kibble- zurek

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