1301.1930 (Aavishkar A. Patel et al.)

Fidelity and dynamics near Dirac points in two-dimensional systems    [PDF]

Aavishkar A. Patel, Shraddha Sharma, Amit Dutta

We study quantum fidelity and dynamics near quantum critical points (QCPs) of the two-dimensional (2-D) Dirac Hamiltonian of graphene (the gapped to gapless transition induced by a mass term) and the 2-D BHZ Hamiltonian of HgTe/CdTe quantum wells (the topological to trivial insulator transition). For the two-dimensional Dirac Hamiltonian, we encounter marginal behaviour of the ground state fidelity near the Dirac point, which is displayed in the absence of a sharp dip in the ground state fidelity (or equivalently the weak logarithmic divergence of the fidelity susceptibility). There is also a logarithmic correction to the proposed scaling of fidelity in the thermodynamic limit. We then study the dynamics of the edge states of the 2-D BHZ Hamiltonian in a ribbon geometry following a sudden quench to the QCP. The effective edge state Hamiltonian is a collection of decoupled two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Lochschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.

View original: http://arxiv.org/abs/1301.1930