Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps

摘要

A sudden quantum quench of a Bloch band from one topological phase towardanother has been shown to exhibit an intimate connection with the notion of adynamical quantum phase transition (DQPT), where the returning probability ofthe quenched state to the initial state---i.e. the Loschmidt echo---vanishes atcritical times $\{t^{*}\}$. Analytical results so far are limited to two-bandmodels, leaving the exact relation between topology and DQPT unclear. In thiswork, we show that for a general multi-band system, a robust DQPT relies on theexistence of nodes (i.e. zeros) in the wavefunction overlap between the initialband and the post-quench energy eigenstates. These nodes are topologicallyprotected if the two participating wavefunctions have distinctive topologicalindices. We demonstrate these ideas in detail for both one and two spatialdimensions using a three-band generalized Hofstadter model. We also discusspossible experimental observations.