Computational Methods

Computational techniques used by QAtlas to evaluate and verify exact results, with physical justification for each approach.

Contents

• Transfer Matrix – row-to-row transfer matrix for classical partition functions ($Z = \text{tr}(T^{L_x})$)
• Bloch Hamiltonian – momentum-space diagonalization of tight-binding models on periodic lattices
• Exact Diagonalization – full $2^N$ Hilbert-space diagonalization for small spin systems
• Jordan–Wigner Transformation – mapping spin chains to free fermions (TFIM BdG solution)
• Automatic Differentiation – thermodynamic quantities from $\partial(\ln Z)/\partial\beta$ via ForwardDiff
• Calabrese–Cardy Formula – entanglement entropy scaling and central charge extraction at quantum critical points