Download presentation
Presentation is loading. Please wait.
1
U NIVERSALITY AND D YNAMIC L OCALIZATION IN K IBBLE -Z UREK Michael Kolodrubetz Boston University In collaboration with: B.K. Clark, D. Huse (Princeton) A. Polkovnikov, A. Katz (BU)
2
K IBBLE -Z UREK S CALING Disordered Ordered
3
K IBBLE -Z UREK SCALING Ramp rate Kibble-Zurek Ramp through the critical point at a constant, finite rate
4
K IBBLE -Z UREK SCALING Ramp rate
5
K IBBLE -Z UREK SCALING Ramp rate
6
K IBBLE -Z UREK SCALING Ramp rate
7
K IBBLE -Z UREK SCALING Ramp rate Fall out of equilibrium
8
K IBBLE -Z UREK SCALING Ramp rate Fall out of equilibrium
9
K IBBLE -Z UREK SCALING Ramp rate Slower
10
K IBBLE -Z UREK SCALING Ramp rate Slower
11
K IBBLE -Z UREK SCALING Ramp rate Slower
12
K IBBLE -Z UREK SCALING Ramp rate Slower
13
K IBBLE -Z UREK SCALING Ramp rate Slower
14
K IBBLE -Z UREK SCALING Recent work: Kibble-Zurek ramps show non-equilibrium scaling (in the limit of slow ramps) [Chandran et. al., Deng et. al., etc.]
15
K IBBLE -Z UREK SCALING Recent work: Kibble-Zurek ramps show non-equilibrium scaling (in the limit of slow ramps) More predictions than just defect production! [Chandran et. al., Deng et. al., etc.]
16
K IBBLE -Z UREK SCALING Excess heat
17
K IBBLE -Z UREK SCALING
20
Schrödinger Equation OR Observable
21
K IBBLE -Z UREK SCALING Schrödinger Equation OR Observable Fixed
22
K IBBLE -Z UREK SCALING Schrödinger Equation OR Observable Fixed Universal dynamics! =
23
T RANSVERSE - FIELD I SING CHAIN
24
Paramagnet (PM) Ferromagnet (FM)
25
T RANSVERSE - FIELD I SING CHAIN Paramagnet (PM) Ferromagnet (FM)
26
K IBBLE -Z UREK SCALING Ramp rate Slower
27
K IBBLE -Z UREK SCALING Ramp rate Slower
28
K IBBLE -Z UREK SCALING Excess heat
29
K IBBLE -Z UREK SCALING
34
Dynamics does not depend on ramp rate!
35
O UTLINE Part I: Universality of Kibble-Zurek scaling Dynamics near QCP gives non-equilibrium critical scaling theory Part II: Kibble-Zurek with a dynamic field
36
O UTLINE 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
37
U NIVERSALITY Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)
38
U NIVERSALITY Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)
39
U NIVERSALITY or Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)
40
U NIVERSALITY or Ramp the tilt linearly in time Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)
41
U NIVERSALITY or Ramp the tilt linearly in time: Solve numerically with DMRG Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)
42
U NIVERSALITY
47
Dynamics are universal!
48
O UTLINE 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
49
O UTLINE 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
50
N ON - EQUILIBRIUM PROPERTIES Spin-spin correlation function
51
N ON - EQUILIBRIUM PROPERTIES Thermal
52
N ON - EQUILIBRIUM PROPERTIES Kibble-Zurek Thermal
53
N ON - EQUILIBRIUM PROPERTIES Kibble-Zurek Thermal Antiferromagnetic
54
N ON - EQUILIBRIUM PROPERTIES Antiferromagnetic
55
O UTLINE 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
56
O UTLINE 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
57
O UTLINE 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
58
D YNAMIC -F IELD K IBBLE -Z UREK
62
“Inflaton” “Higgs field”
63
D YNAMIC -F IELD K IBBLE -Z UREK “Inflaton” “Higgs field”
64
D YNAMIC -F IELD K IBBLE -Z UREK
105
When does field get trapped?
106
D YNAMIC -F IELD K IBBLE -Z UREK
107
Mass density
108
D YNAMIC -F IELD K IBBLE -Z UREK Mass density
109
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Trapped
110
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Ising: Higgs: Trapped
111
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Ising: Higgs: Trapped
112
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Ising: Higgs: Trapped
113
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Ising: Higgs: Trapped
114
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Ising: Higgs: Trapped
115
D YNAMIC -F IELD K IBBLE -Z UREK Mass density Ising: Higgs: Trapped
116
D YNAMIC -F IELD K IBBLE -Z UREK
120
Dynamics dominated by critical behavior
121
D YNAMIC -F IELD K IBBLE -Z UREK
131
Fluctuations around QCP
132
D YNAMIC -F IELD K IBBLE -Z UREK
135
Fluctuations around QCP
136
D YNAMIC -F IELD K IBBLE -Z UREK Fluctuations around QCP
137
D YNAMIC -F IELD K IBBLE -Z UREK Fluctuations around QCP
138
O UTLINE 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
139
O UTLINE 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.
140
O UTLINE 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?
141
O UTLINE 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
142
D YNAMIC -F IELD K IBBLE -Z UREK Scaling hypothesis Initial momentum is the relevant scale for dynamics
143
D YNAMIC -F IELD K IBBLE -Z UREK Scaling hypothesis Initial momentum is the relevant scale for dynamics
144
D YNAMIC -F IELD K IBBLE -Z UREK Scaling hypothesis Initial momentum is the relevant scale for dynamics
145
O UTLINE 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
146
O UTLINE 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?
147
O UTLINE 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
148
O UTLINE 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
149
D YNAMIC -F IELD K IBBLE -Z UREK
150
O UTLINE 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…
151
S UMMARY Part I: Universality of Kibble-Zurek scaling Part II: Kibble-Zurek with a dynamic field
152
T RANSVERSE - FIELD I SING CHAIN
153
phase
154
T RANSVERSE - FIELD I SING CHAIN phase
155
E QUILIBRIUM SCALING “Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
156
E QUILIBRIUM SCALING Low energy, long wavelength theory? “Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
157
E QUILIBRIUM SCALING Low energy, long wavelength theory “Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied
158
K IBBLE -Z UREK SCALING
159
Low energy, long wavelength theory?
160
K IBBLE -Z UREK SCALING Low energy, long wavelength theory?
161
K IBBLE -Z UREK SCALING Low energy, long wavelength theory
162
N ON - EQUILIBRIUM PROPERTIES
169
Inverted
170
D YNAMIC -F IELD I SING CHAIN Basic idea: Add (classical) dynamics to the transverse field
171
D YNAMIC -F IELD I SING CHAIN Basic idea: Add (classical) dynamics to the transverse field
172
D YNAMIC -F IELD I SING CHAIN Basic idea: Add (classical) dynamics to the transverse field “Friction” = back-action of spins on field
173
D YNAMIC -F IELD I SING 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
174
D YNAMIC -F IELD I SING 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?
Similar presentations
