2026/07/20 by Meng Zeng, Shuai Yin, Roderich Moessner
#cond-mat.str-el #cond-mat.stat-mech #quant-ph
We revisit the problem of real-time quantum dynamics of the paradigmatic two dimensional transverse-field Ising model using the recently developed fuzzy sphere regularization scheme. By linearly ramping the transverse field from the paramagnetic phase to criticality, we study the finite-time scaling behavior of the squared order parameter ⟨ mz2 ⟩, the excitation energy density Q, and the two-point correlation function of mz. We establish numerically that, at intermediate quench rate, ⟨ mz2 ⟩ follows the conventional Kibble-Zurek prediction set by the critical exponents of the 3D Ising universality class, and the correlation function exhibits the expected exponential decay whose correlation length can be used to estimate the non-universal scaling coefficient in the freeze-out time/length. In contrast, the excitation energy density Q does not reach the same scaling regime at available system sizes due to large effective finite-size gap from symmetry-enforced level sparsity in the energy spectrum. At slow quench rates the universal quasi-adiabatic scaling for both ⟨ mz2 ⟩ and Q is recovered. Since the fuzzy sphere construction can realize not only the Ising conformal field theory (CFT), but a broad family of (2+1)d CFTs, our results establish a route to the real-time critical dynamics of strongly coupled CFTs that are otherwise computationally challenging to study.