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Abstract:
We analyze the near-adiabatic dynamics in a ramp through the critical point (CP) of the classical transverse field Ising chain. This is motivated, conceptually, by the fact that this CP-unlike its quantum counterpart-experiences no thermal or quantum fluctuations, and technically by the tractability of its effective model. For a "half ramp" from a ferromagnet to the CP, the longitudinal and transverse magnetizations scale as tau(-1/3) and tau(-2/3), respectively, with 1/tau the ramp rate, in accord with Kibble-Zurek theory. For ferro- to paramagnetic ramps across the CP, however, they stay closer, tau(-2/3) and tau(-1), to adiabaticity. This adiabaticity enhancement compared to the half ramp is understood by casting the dynamics in the paramagnet in the form of a non-Hermitian Dirac Hamiltonian, with the CP playing the role of an exceptional point, opening an additional decay channel.
