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

Fall out ofequilibrium

Ramp rate

Fall out ofequilibrium

Ramp rate

Slower

Ramp rate

Slower

Ramp rate

Slower

Ramp rate

Slower

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

Universaldynamics!=

TRANSVERSE-FIELD ISING CHAIN

Paramagnet (PM) Ferromagnet (FM)

Ramp rate

Slower

Ramp rate

Slower

Excess heat

Dynamics does not depend on ramp

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

Ramp the tilt linearly in time

UNIVERSALITY

Ramp the tilt linearly in time: Solve numerically

with DMRG

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

Thermal

Kibble-Z

Thermal

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”

“Inflaton”

“Higgs field”

When does field get trapped?

Mass density

Trapped

Mass density

Ising:

Higgs:

Trapped

Mass density

Ising:

Higgs:

Trapped

Mass density

Ising:

Higgs:

Trapped

Mass density

Ising:

Higgs:

Trapped

Mass density

Ising:

Higgs:

Trapped

Mass density

Ising:

Higgs:

Trapped

Dynamics dominated by critical behavior

DYNAMIC-FIELD KIBBLE-ZUREKF

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

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

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

What happens when field tries to

pass through the critical point?

Universality and Dynamic Localization in Kibble- Zurek

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