Eigenstate Thermalization in a Spin Chain

This simulator exactly diagonalizes a small (N = 8, Hilbert space dimension 256) mixed-field Ising spin chain and uses the real eigenbasis to unitarily evolve a far-from-equilibrium initial state — a domain wall or a Néel pattern. Watching the row of spins relax, you can directly see the central claim of the Eigenstate Thermalization Hypothesis at work: a closed quantum system obeying only the Schrödinger equation can still make local observables look thermal, because the individual energy eigenstates themselves already encode a thermal-looking expectation value once the system is chaotic. Sliding the h_z field from 0 (integrable, free-fermion) to about 0.5 (quantum-chaotic) turns the eigenstate scatter cloud from wide and scattered into a narrow, smooth band — and the relaxation of the spin chain from partial/oscillatory into genuine thermalization.