Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain

Abstract

The transverse field in the quantum Ising chain is linearly ramped from the para- to the ferromagnetic phase across the quantum critical point at a rate characterized by a quench time ${\tau }_Q$. We calculate a connected kink-kink correlator in the final state at zero transverse field. The correlator is a sum of two terms: a negative (anti-bunching) Gaussian that depends on the Kibble-Zurek (KZ) correlation length only and a positive term that depends on a second longer scale of length. The second length is made longer by dephasing of the state excited near the critical point during the following ramp across the ferromagnetic phase. This interpretation is corroborated by considering a linear ramp that is halted in the ferromagnetic phase for a finite waiting time and then continued at the same rate as before the halt. The extra time available for dephasing increases the second scale of length that asymptotically grows linearly with the waiting time. The dephasing also suppresses magnitude of the second term making it negligible for waiting times much longer than ${\tau }_Q$. The same dephasing can be obtained with a smooth ramp that slows down in the ferromagnetic phase. Assuming sufficient dephasing we obtain also higher order kink correlators and the ferromagnetic correlation function.

10 pages; last two paragraphs added in Sec. IX; version to appear in PRB

References in corpus (21)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Universal adiabatic dynamics across a quantum critical point
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Defect production in non-linear quench across a quantum critical point
• Emergence of coherence and the dynamics of quantum phase transitions
• Exact results for quench dynamics and defect production in a two-dimensional model
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
• Kibble-Zurek mechanism in a quenched ferromagnetic Bose-Einstein condensate
• Defect formation beyond Kibble-Zurek mechanism and holography
• Vortex quantum creation and winding number scaling in a quenched spinor Bose gas
• Universal far-from-equilibrium Dynamics of a Holographic Superconductor
• Spontaneous nucleation of structural defects in inhomogeneous ion chains
• Realization of inverse Kibble-Zurek scenario with trapped Bose gases

Cited by in corpus (2)

• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Kibble-Zurek scaling in the quantum Ising chain with a time-periodic perturbation