Quantum complexity and topological phases of matter
Paweł Caputa, Sinong Liu
Abstract
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.
Topics & Concepts
Topological complexityPhysicsHamiltonian (control theory)QuantumTopology (electrical circuits)Topological entropy in physicsState of matterTopological orderBasis (linear algebra)Statistical physicsTheoretical physicsWork (physics)Topological quantum numberQuantum mechanicsMathematicsPure mathematicsGeometryCombinatoricsMathematical optimizationQuantum many-body systemsTopological Materials and PhenomenaQuantum and electron transport phenomena