Interactive 2D Chern number calculator using the Fukui–Hatsugai–Suzuki discretized Berry curvature method. Drag m to traverse topological phase transitions in real time.
Adjust the mass parameter m and hopping amplitude t₁ to observe topological phase transitions. The Chern number is computed via discrete plaquette integration over the Brillouin zone.
Interactive 2D Chern number calculator using the Fukui–Hatsugai–Suzuki discretized Berry curvature method. Drag m to traverse topological phase transitions in real time.
The 2D Chern insulator is a minimal topological model exhibiting a quantized Hall conductance without an external magnetic field — a cornerstone of modern topological materials science.
The model uses a two-band Hamiltonian H(k) = d(k)·σ on a 2D square lattice, where d = (sin kₓ, sin k_y, m + t₁(cos kₓ + cos k_y)). Topology is encoded in the winding of d around the origin.
The Chern number is a topological invariant C ∈ ℤ computed by integrating Berry curvature over the Brillouin zone. C = ±1 signals a topologically non-trivial phase; C = 0 is trivial.
The Fukui–Hatsugai–Suzuki algorithm computes C via a discrete lattice of U(1) link variables across an N×N k-mesh, accumulating plaquette phases. This avoids gauge-fixing issues and converges rapidly.
Gap closings at m = 0 and m = ±2t₁ mark topological phase transitions where C jumps discontinuously. The Berry curvature map shows intense localized flux at these critical momenta.
k-mesh Points
Phase Regions
Chern Number Range
Compute Latency