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

Abstract

A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state---i.e. the Loschmidt echo---vanishes at critical times $\{t^{\ast }\}$. Analytical results so far are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this work, we show that for a general multi-band system, a robust DQPT relies on the existence of nodes (i.e. zeros) in the wavefunction overlap between the initial band and the post-quench energy eigenstates. These nodes are topologically protected if the two participating wavefunctions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.

5 pages, 2 figures, plus supplementary. v2: fixed typos, updated references, added a new appendix on a 1D 3-band model exhibiting symmetry-protected DQPT. To appear in Phys. Rev. Lett

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Many body localization and thermalization in quantum statistical mechanics
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Fluctuation theorems: Work is not an observable
• Ultracold atoms out of equilibrium
• Quench dynamics across quantum critical points
• Topological classification of dynamical phase transitions
• First order dynamical phase transitions
• Optimal non-linear passage through a quantum critical point
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Direct measurement of topological invariants in optical lattices
• Direct Probe of Topological Order for Cold Atoms
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model

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