Quantum complexity and topological phases of matter

In this work, we find that the complexity of quantum many-body states, defined as a spread in the Krylov basis, may serve as a probe that distinguishes topological phases of matter. We illustrate this analytically in one of the representative examples, the Su-Schrieffer-Heeger model, finding that spread complexity becomes constant in the topological phase. Moreover, in the same setup, we analyze exactly solvable quench protocols where the evolution of the spread complexity shows distinct dynamical features depending on the topological vs nontopological phase of the initial state as well as the quench Hamiltonian.

Automated summary

In this study, the complexity of quantum many-body states is found to distinguish topological phases of matter. The Su-Schrieffer-Heeger model is used to illustrate that spread complexity remains constant in the topological phase. Additionally, exact solvable quench protocols are analyzed, revealing distinct dynamical features of spread complexity depending on the initial state's topological phase and the quench Hamiltonian.