Speaker
Description
Krylov complexity - a measure of operator growth through Heisenberg time evolution via the Lanczos-constructed Krylov basis - has proven useful as a probe of quantum chaos and dynamical phase transitions, but we ask whether it can also detect topological phase transitions, motivated by the fact that both the change in level statistics and the change in underlying geometry accompanying such transitions should leave an imprint on the Krylov construction. We test this on two toy models: the Kitaev chain, where we compute K-complexity for the circuit connecting the free-fermion and Kitaev ground states across the topological/trivial phase boundary using a BdG diagonalization and su(2,ℂ) coherent-state formalism; and a pair of linearly coupled Bateman oscillators, where K-complexity resolves the onset of the PT-symmetric regime. Our results suggest Krylov complexity is a computationally tractable order parameter for topological phase transitions, extending its role beyond chaos diagnostics into ground-state topology.