universality and dynamic localization in kibble- zurek
DESCRIPTION
Universality and Dynamic Localization in Kibble- Zurek. Michael Kolodrubetz Boston University In collaboration with: B.K. Clark, D. Huse (Princeton) A. Polkovnikov , A. Katz (BU). Kibble- Zurek Scaling. Disordered. Ordered. Kibble- Zurek scaling. Ramp rate. - PowerPoint PPT PresentationTRANSCRIPT
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
KIBBLE-ZUREK SCALING
Ramp rate
Kibble-ZurekRamp through the critical
point at a constant, finite rate
KIBBLE-ZUREK SCALING
Ramp rate
KIBBLE-ZUREK SCALING
Ramp rate
KIBBLE-ZUREK SCALING
Ramp rate
KIBBLE-ZUREK SCALING
Ramp rate
Fall out ofequilibrium
KIBBLE-ZUREK SCALING
Ramp rate
Fall out ofequilibrium
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Recent work: Kibble-Zurek rampsshow non-equilibrium scaling (in the limit of slow ramps)
[Chandran et. al., Deng et. al., etc.]
KIBBLE-ZUREK SCALING
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.]
KIBBLE-ZUREK SCALING
Excess heat
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
SchrödingerEquation
ORObservable
KIBBLE-ZUREK SCALING
SchrödingerEquation
ORObservable
Fixed
KIBBLE-ZUREK SCALING
SchrödingerEquation
ORObservable
Fixed
Universaldynamics!=
TRANSVERSE-FIELD ISING CHAIN
TRANSVERSE-FIELD ISING CHAIN
Paramagnet (PM) Ferromagnet (FM)
TRANSVERSE-FIELD ISING CHAIN
Paramagnet (PM) Ferromagnet (FM)
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Ramp rate
Slower
KIBBLE-ZUREK SCALING
Excess heat
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
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
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Are the results universal?
Part II: Kibble-Zurek with a dynamic field
UNIVERSALITY
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
UNIVERSALITY
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
UNIVERSALITY
or
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
UNIVERSALITY
or
Ramp the tilt linearly in time
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
UNIVERSALITY
or
Ramp the tilt linearly in time: Solve numerically
with DMRG
TheorySachdev et al. (2002)ExperimentGreiner group (Harvard)Nagerl group (Innsbruck)
UNIVERSALITY
UNIVERSALITY
UNIVERSALITY
UNIVERSALITY
UNIVERSALITY
UNIVERSALITY
Dynamics are
universal!
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs
Part II: Kibble-Zurek with a dynamic field
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Non-trivial scaling functions
Part II: Kibble-Zurek with a dynamic field
NON-EQUILIBRIUM PROPERTIES
Spin-spin correlation function
NON-EQUILIBRIUM PROPERTIES
Thermal
NON-EQUILIBRIUM PROPERTIES
Kibble-Z
urek
Thermal
NON-EQUILIBRIUM PROPERTIES
Kibble-Z
urek
Thermal
Antiferromagnetic
NON-EQUILIBRIUM PROPERTIES
Antiferromagnetic
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
non-equilibrium critical scaling theory Dynamics are universal to Ising-like QPTs Long-time dynamics are athermal
Part II: Kibble-Zurek with a dynamic field
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
“Inflaton”
“Higgs field”
DYNAMIC-FIELD KIBBLE-ZUREK
“Inflaton”
“Higgs field”
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
When does field get trapped?
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
Mass density
Ising:
Higgs:
Trapped
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
Dynamics dominated by critical behavior
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREK
DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
DYNAMIC-FIELD KIBBLE-ZUREKF
luct
ua
tion
s a
rou
nd
QC
P
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
Should work equally well for Higgs, etc.
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
Should work equally well for Higgs, etc. Do dynamics show scaling collapse?
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
Should work equally well for Higgs, etc. Do dynamics show scaling collapse?
Expect scaling for
DYNAMIC-FIELD KIBBLE-ZUREK
Scaling hypothesisInitial momentum is the
relevant scale for dynamics
DYNAMIC-FIELD KIBBLE-ZUREK
Scaling hypothesisInitial momentum is the
relevant scale for dynamics
DYNAMIC-FIELD KIBBLE-ZUREK
Scaling hypothesisInitial momentum is the
relevant scale for dynamics
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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 Effect of ground state potential?
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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 Effect of ground state potential
Is RG relevant
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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 Effect of ground state potential
Is RG relevant Trapping in certain regimes
DYNAMIC-FIELD KIBBLE-ZUREK
OUTLINE
Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives
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
Part II: Kibble-Zurek with a dynamic field
TRANSVERSE-FIELD ISING CHAIN
TRANSVERSE-FIELD ISING CHAIN
phase
TRANSVERSE-FIELD ISING CHAIN
phase
EQUILIBRIUM SCALING
“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
EQUILIBRIUM SCALING
Low energy, long wavelength theory?
“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
EQUILIBRIUM SCALING
Low energy, long wavelength theory
“Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
KIBBLE-ZUREK SCALING
KIBBLE-ZUREK SCALING
Low energy, long wavelength theory?
KIBBLE-ZUREK SCALING
Low energy, long wavelength theory?
KIBBLE-ZUREK SCALING
Low energy, long wavelength theory
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
NON-EQUILIBRIUM PROPERTIES
Inverted
DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
“Friction” = back-action of spins on field
DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse field
“Friction” = back-action of spins on field Mass is extensive ( ) Mean-field coupling between field and spins
DYNAMIC-FIELD ISING CHAIN
Basic idea: Add (classical) dynamics to the transverse 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?