Anomalous Dynamical Scaling at Topological Quantum Criticality

We study the nonequilibrium driven dynamics at topologically nontrivial quantum critical points (QCPs),and find that topological edge modes at criticality give rise to anomalous universal dynamical scaling behavior. By analyzing the driven dynamics of bulk and boundary order parameters at topologically distinct Ising QCPs, we demonstrate that, while the bulk dynamics remain indistinguishable and follow standard Kibble Zurek (KZ) scaling, the anomalous boundary dynamics is unique to topological criticality, and its explanation goes beyond the traditional KZ mechanism. To elucidate the unified origin of this anomaly, we further study the dynamics of defect production at topologically distinct QCPs in free-fermion models and demonstrate similar anomalous universal scaling exclusive to topological criticality. These findings establish the existence of anomalous dynamical scaling arising from the interplay between topology and driven dynamics, challenging standard paradigms of quantum critical dynamics.

💡 Research Summary

The authors investigate non‑equilibrium dynamics when a system is driven across quantum critical points (QCPs) that are topologically non‑trivial. They focus on two one‑dimensional Ising‑type models that share the same bulk critical exponents (the 1+1 D Ising universality class) but differ in their boundary topology: the transverse‑field Ising (TFI) chain, which has a trivial boundary, and the cluster‑Ising (CI) chain, which hosts robust edge modes even at criticality (the so‑called Ising* QCP).

Both models are subjected to a linear ramp of the control parameter λ(t)=λ_c+(λ_c−λ_i) R t, with R the quench rate, driving the system from a ferromagnetic phase to the critical point. Open boundary conditions allow the authors to monitor bulk magnetization m_b (site L/2) and boundary magnetization m_s (site 1). Using Gaussian‑state techniques they compute the scaling of these observables for system sizes up to L = 256 and a wide range of R.

According to the standard Kibble‑Zurek (KZ) picture, the freeze‑out time scales as (\hat t\propto R^{-z\nu/(1+z\nu)}) and the distance to criticality as (\hat\epsilon\propto R^{1/(1+z\nu)}). An observable that scales in equilibrium as (\epsilon^{\beta}) should therefore follow (O(R)\propto R^{\beta/(1+z\nu)}). For the bulk magnetization the equilibrium exponent is (\beta_b=1/8) and with z = ν = 1 the prediction is (m_b\propto R^{1/16}). Numerical data for both TFI and CI confirm this conventional KZ scaling.

The boundary magnetization, however, behaves differently. In the TFI chain the equilibrium boundary exponent is (\beta_s=1/2); inserting the same z and ν yields the KZ prediction (m_s\propto R^{1/4}), which is indeed observed. In stark contrast, the CI chain exhibits a linear scaling (m_s\propto R) (exponent ≈ 1), completely incompatible with the KZ formula even if one uses the equilibrium boundary exponent (\beta_s=1) obtained from conformal boundary theory.

To resolve this discrepancy the authors propose a generalized scaling law
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