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We solve for the time-dependent finite-size scaling functions of the 1D transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point.
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We note that, in principle, the theory of Toeplitz determinants [ 27 ] can be used to analytically solve for the correlation function in the limit x ≫ 1 x\gg 1
Cited in the paper.
We note two points about observing dephasing in practice. First, our arguments only hold when taking the long time limit while remaining near the QCP ( λ ≪ 1 \lambda\ll 1 ) to stay in the scaling regime. This limit is difficult to achieve, and is compounded by disorder, which becomes more important in the slow ramp, long time limit. Second, one must know the exact location of the QCP for the cubic ramp; a slight “miss” would allow one to linearize about the actual QCP. The slower the ramp, the more accurately one needs to know the QCP to see cubic scaling
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There is an overall non-universal scaling between the TFI and MITP models, given empirically by v MITP = 4.84 v TFI v_{\mathrm{MITP}}=4.84v_{\mathrm{TFI}} , G MITP = 0.196 G TFI G_{\mathrm{MITP}}=0.196G_{\mathrm{TFI}} , and t MITP = 0.557 t TFI t_{\mathrm{MITP}}=0.557t_{\mathrm{TFI}} . All values in fig. 1
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Our analysis neglects the effect of disorder and open boundary conditions, which will need to be included to fully describe the Harvard experiment. See the supplemental information for brief analysis of open boundary conditions
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