Quantum mechanics

Ergodicity

Spin (aerodynamics)

Statistics

Entropy (arrow of time)

Markov chain

Eigenvalues and eigenvectors

Statistical physics

Random matrix

Thermodynamics

Physics

Quantum entanglement

Transition point

Mathematics

Condensed matter physics

Quantum

Stochastic matrix

Physical review. B./Physical review. B

We study disorder-induced ergodicity breaking transition in high-energy eigenstates of interacting spin-1/2 chains. Using exact diagonalization, we introduce a cost function approach to quantitatively compare different scenarios for the eigenstate transition. We study ergodicity indicators such as the eigenstate entanglement entropy and the spectral level spacing ratio, and we consistently find that an (infinite-order) Berezinskii-Kosterlitz-Thouless transition yields a lower cost function when compared to a finite-order transition. Interestingly, we observe that the ergodicity breaking transition in systems studied by exact diagonalization (with around 20 lattice sites) takes place at disorder values lower than those reported in previous works. As a consequence, the crossing point in finite systems exhibits nearly thermal properties, i.e., ergodicity indicators at the transition are close to the random matrix theory predictions.

Ergodicity breaking transition in finite disordered spin chains