Universal Landau Zener behavior in the dynamics of topological phase transitions

Ge Yang, Marcos Rigol

In finite systems driven unitarily across topological phase transitions, the Chern number and the Bott index have been found to exhibit different behaviors depending on the boundary conditions and on the commensurability of the lattice. For periodic boundary conditions, the Chern number does not change for finite commensurate lattices (or in the thermodynamic limit). On the other hand, the Chern number can change for incommensurate lattices with periodic boundary conditions and the Bott index can change for lattices with open boundary conditions. Here we show that the scalings of the fields at which those two indices change exhibit Landau-Zener and near-adiabatic regimes depending on the speed at which the strength of the drive is ramped up and on the system size. Those regimes are preceded by a regime in which the topological indices do not change. The latter is the only regime that, for nonvanishing ramp speeds, survives in the thermodynamic limit. We then show that the dc Hall response can be used to detect topological phase transitions independently of the behavior of the topological indices.

M. A. Contínentino

Bogdan Damski

It can be shown that the dynamics of the Landau-Zener model can be accurately described in terms of the Kibble-Zurek theory of the topological defect production in nonequilibrium phase transitions. The simplest quantum model exhibiting the Kibble-Zurek mechanism is presented. A new intuitive description of Landau-Zener dynamics is found.

Robert-Jan Slager

Menghua Deng, Zhoujian Sun, Fuxiang Li

The Kibble-Zurek mechanism predicts a universal scaling behavior of the defect production when a system is slowly quenched across a critical phase transition point. Here, we discover that the universal scaling behavior across a higher-order topological phase transition does not conform to the traditional Kibble-Zurek mechanism. To explain the anomalous scaling exponent, we develop a solvable Landau-Zener model that takes into account the role of topological edge band that dominates the phase transition. For a two-dimensional boundary-obstructed higher-order topological system, the Kibble-Zurek scaling must be modified to adopt the effective dimension of topological edge band instead of the real physical dimension. We also find that across the boundary-obstructed higher-order topological phase transition, boundary conditions can drastically modify the scaling behaviors. For comparison, we investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with physical dimension.