Common Dynamic Scaling of 2D Quantum Ising Transition on the Fuzzy Sphere

arXiv:2607.18028v1 Announce Sort: cross
Summary: We revisit the issue of textit{real-time} quantum dynamics of the paradigmatic two dimensional transverse-field Ising mannequin utilizing the just lately developed fuzzy sphere regularization scheme. By linearly ramping the transverse area from the paramagnetic section to criticality, we examine the finite-time scaling habits of the squared order parameter $langle m_z^2 rangle$, the excitation power density $Q$, and the two-point correlation perform of $m_z$. We set up numerically that, at intermediate quench fee, $langle m_z^2 rangle$ follows the traditional Kibble-Zurek prediction set by the vital exponents of the $3$D Ising universality class, and the correlation perform reveals the anticipated exponential decay whose correlation size can be utilized to estimate the non-universal scaling coefficient within the freeze-out time/size. In distinction, the excitation power density $Q$ doesn’t attain the identical scaling regime at accessible system sizes on account of massive efficient finite-size hole from symmetry-enforced degree sparsity within the power spectrum. At gradual quench charges the common quasi-adiabatic scaling for each $langle m_z^2 rangle$ and $Q$ is recovered. Because the fuzzy sphere development can notice not solely the Ising conformal area idea (CFT), however a broad household of $(2+1)d$ CFTs, our outcomes set up a path to the real-time vital dynamics of strongly coupled CFTs which might be in any other case computationally difficult to review.



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