Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems

Abstract

z r ∆h(r), whereσ α r (α = x, y, z) is the Pauli operator on site r ∈ Ω N . While the previous works regarding the quantum quench focused only on the final state, we here study the quench susceptibility,which quantifies the difference of the expectation values of the k-component of magnetization,m k = arXiv:1911.02456v2 [cond-mat.stat-mech] 3 Dec 2019 in isolated quantum systems: Supplemental Material A. Quench susceptibility

Dissipative spin dynamics in hot quantum paramagnets

“…Whether or not such a non-analytic contribution proportional to δ ω,0 survives for finite exchange coupling is closely related to the ergodicity of the system and the distinction between the isolated (Kubo) susceptibility and the isothermal susceptibility [45][46][47][48][49]. Note that for k = 0 the zero-frequency limit of the finite-frequency thermal spin-spin correlation function G(k = 0, iω) gives the isolated (Kubo) susceptibility, which in general does not agree with the isothermal susceptibility defined via the derivative of the magnetization with respect to an external magnetic field at constant temperature [45][46][47][48][49]. However, as recently shown by Chiba et al [49], under conditions similar to the eigenstate thermalization hypothesis [50], at finite momentum k = 0 all static susceptibilities agree.…”

“…Note that for k = 0 the zero-frequency limit of the finite-frequency thermal spin-spin correlation function G(k = 0, iω) gives the isolated (Kubo) susceptibility, which in general does not agree with the isothermal susceptibility defined via the derivative of the magnetization with respect to an external magnetic field at constant temperature [45][46][47][48][49]. However, as recently shown by Chiba et al [49], under conditions similar to the eigenstate thermalization hypothesis [50], at finite momentum k = 0 all static susceptibilities agree. This rules out a non-analytic contribution to the thermal spin-spin correlation function G(k, iω) similar to Eq.…”