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 Kibble-Zurek Ramp 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 of equilibrium KIBBLE-ZUREK SCALING Ramp rate Fall out of equilibrium KIBBLE-ZUREK SCALING Ramp rate KIBBLE-ZUREK SCALING Ramp rate KIBBLE-ZUREK SCALING Ramp rate KIBBLE-ZUREK SCALING Ramp rate KIBBLE-ZUREK SCALING Ramp rate KIBBLE-ZUREK SCALING Recent work: Kibble-Zurek ramps show non-equilibrium scaling (in the limit of slow ramps) [Chandran et. al., Deng et. al., etc.] KIBBLE-ZUREK 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.] KIBBLE-ZUREK SCALING Excess heat KIBBLE-ZUREK SCALING KIBBLE-ZUREK SCALING KIBBLE-ZUREK SCALING KIBBLE-ZUREK SCALING Schrödinger Equation OR Observable KIBBLE-ZUREK SCALING Schrödinger Equation OR Observable Fixed KIBBLE-ZUREK SCALING Schrödinger Equation OR Observable Fixed = Universal dynamics! 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 KIBBLE-ZUREK SCALING Ramp rate 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 Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck) UNIVERSALITY Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck) UNIVERSALITY or Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck) UNIVERSALITY Ramp the tilt linearly in time or Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck) UNIVERSALITY Ramp the tilt linearly in time: Solve numerically with DMRG or Theory Sachdev et al. (2002) Experiment Greiner 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 NON-EQUILIBRIUM PROPERTIES NON-EQUILIBRIUM PROPERTIES 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 “Higgs field” “Inflaton” DYNAMIC-FIELD KIBBLE-ZUREK “Higgs field” “Inflaton” 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: Trapped Higgs: DYNAMIC-FIELD KIBBLE-ZUREK Mass density Ising: Trapped Higgs: DYNAMIC-FIELD KIBBLE-ZUREK Mass density Ising: Trapped Higgs: DYNAMIC-FIELD KIBBLE-ZUREK Mass density Ising: Trapped Higgs: DYNAMIC-FIELD KIBBLE-ZUREK Mass density Ising: Trapped Higgs: DYNAMIC-FIELD KIBBLE-ZUREK Mass density Ising: Trapped Higgs: 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 Fluctuations around QCP DYNAMIC-FIELD KIBBLE-ZUREK DYNAMIC-FIELD KIBBLE-ZUREK DYNAMIC-FIELD KIBBLE-ZUREK DYNAMIC-FIELD KIBBLE-ZUREK Fluctuations around QCP DYNAMIC-FIELD KIBBLE-ZUREK Fluctuations around QCP DYNAMIC-FIELD KIBBLE-ZUREK Fluctuations around QCP 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 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 hypothesis Initial momentum is the relevant scale for dynamics DYNAMIC-FIELD KIBBLE-ZUREK Scaling hypothesis Initial momentum is the relevant scale for dynamics DYNAMIC-FIELD KIBBLE-ZUREK Scaling hypothesis Initial 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 “Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied Low energy, long wavelength theory? EQUILIBRIUM SCALING “Spin up” (k,-k) unoccupied “Spin down” (k,-k) occupied Low energy, long wavelength theory 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?
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