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

Research Question and Approach

Understanding the real-time dynamics of many-body systems driven through a quantum phase transition is a fundamental challenge in nonequilibrium physics. While Kibble-Zurek (KZ) theory and finite-time scaling (FTS) are well-established in 1D, they are difficult to study in higher dimensions due to the computational costs of simulating strongly correlated systems. This paper investigates whether the fuzzy sphere regularization—a method that preserves SO(3) rotational symmetry and allows for the study of (2+1)d conformal field theories (CFTs)—can serve as a reliable platform for testing these universal scaling laws.

The authors study the 2D transverse-field Ising model by linearly ramping the transverse field toward the critical point. They employ a time-dependent variational principle (TDVP) algorithm, enhanced by bond expansion, to compute the squared order parameter, excitation energy density, and two-point correlation functions.

The study confirms that the fuzzy sphere geometry effectively reproduces universal KZ scaling for the squared magnetization and the two-point correlation function. These observables exhibit clean data collapse consistent with the 3D Ising universality class. By analyzing the correlation function, the authors also extract the non-universal scaling coefficient related to the freeze-out time.

However, the excitation energy density does not follow the predicted scaling at the system sizes currently accessible. The authors attribute this to the high degree of symmetry in the fuzzy sphere construction, which restricts the dynamics to specific sectors and leads to a sparse energy spectrum. This creates a large effective finite-size gap that masks the universal scaling behavior for energy-related quantities. Despite this, the study successfully recovers the expected quasi-adiabatic scaling in the slow-quench limit.