Boundary-induced dynamics in one-dimensional topological systems and memory effects of edge modes

Abstract

Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into the bulk, the density of topological edge modes in the case of transforming to open boundary condition reaches steady states. The steady-state density depends on the transformation rate of the boundary and serves as an illustration of quantum memory effects in topological systems. Moreover, while a link is physically broken as the boundary condition changes, some correlation functions can remain finite across the broken link and keep a record of the initial condition. By testing those phenomena in the non-topological regimes of the two models, none of the interesting signatures of memory effects can be observed. Our results thus contrast the importance of topological properties in boundary-induced dynamics.

Dynamics of two-dimensional topological quadrupole insulator and Chern insulator induced by real-space topological changes

“…The emergence of a steady state is interesting because we do not introduce any explicit dissipation mechanism. Steady states of systems without dissipation have also been found in the dynamics of 1D topological systems after a change in boundary condition 29 .…”

“…The quantum dynamics can be describe by the Heisenberg equation 29 . For an operator A, we have dA dt = −i[A, H].…”

“…We emphasize that the possibility of using the directions of the density ripples to differentiate the underlying configurations is not available in 1D systems because the density ripples spread out to the whole systems, as shown in Ref. 29 . Thus, more interesting physics can be explored in higher-dimensional topological systems with real-space topological configurations as illustrated here.…”

On the adiabatic theorem when eigenvalues dive into the continuum

“…Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit. At the end of the paper we present a short outlook on how our method may be extended to cover other classes of Hamiltonians; details will be given elsewhere.the existence of the so-called spontaneous (adiabatic) pair creation in linear quantum electrodynamics [10,11,15], as well as for memory effects in quantum mesoscopic transport [2,3,4,9].Turning this heuristics into a mathematical statement proved to be a hard problem and boiled down to a proof of various aspects of the adiabatic theorem in the case where the eigenvalue hits the threshold of the continuous spectrum. Accordingly, the existence results are very limited and the proofs are rather technical and often need further assumptions [3,10,11].Our main result states that the survival probability vanishes in the adiabatic limit, i.e.…”

“…the existence of the so-called spontaneous (adiabatic) pair creation in linear quantum electrodynamics [10,11,15], as well as for memory effects in quantum mesoscopic transport [2,3,4,9].…”