Topological Phase Transitions in Finite-size Systems Across Boundary Conditions

Systems driven unitarily across different topological phases seem to exhibit contrary behaviors depending on their boundary conditions [1] and the commensurability of system sizes [2]. In particular, a “no-go” theorem forbidding the change of the Chern number exists for periodic boundary systems. Here we first demonstrate the scaling of dynamical phase transition points in driven periodic boundary systems for different turn-on speeds and incommensurate system sizes, which consist of a Landau-Zener governed regime and an adiabatic following regime. Similar regimes are also identified in the case of open boundary systems, proving that these boundary conditions agree in the thermodynamic limit. Finally, we show that with slow turn-ons the dc Hall response of a driven fermi sea starting from a trivial state does acquire a non-trivial value in a finite-size system, even when the “no-go” theorem applies.

[1] L. D'Alessio and M. Rigol, Nat. Commun. 6, 8336 (2015).
[2] Y. Ge and M. Rigol, Phys. Rev. A. 96, 023610 (2017).