2018/10/08 by Shuangyuan Lu, Jinlong Yu
Physics and Astronomy · #cond-mat.str-el #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.99.033621
published as Phys. Rev. A 99, 033621 (2019) · 7 pages, 4 figures. Comments are welcome
arxiv created 2018/10/08 · arxiv updated 2019/04/03
In a recent work by Gong and Ueda (arXiv:1710.05289), the classification of (1+1)-dimensional quench dynamics for the ten Altland-Zirnbauer classes is achieved, and entanglement-spectrum crossings of the time-dependent states for the topological classes (AIII, DIII, CII, BDI, and D) are discovered as a consequence of the bulk-edge correspondence. We note that, their classification scheme relies on the limit that the energy spectrum of the post-quench Hamiltonian is flat, because any finite band dispersion leads to the break down of time-reversal and chiral symmetries for the parent Hamiltonian (which are used for the classification). We show that, because of the reduction of symmetry by finite energy dispersion, the gapless entanglement-spectrum crossing in the flat-band limit in classes AIII, DIII, and CII is unstable, and could be gapped without closing the bulk gap. The entanglement-spectrum crossing in classes BDI and D is still stable against energy dispersion. We show that the quench process for classes BDI and D can be understood as a ℤ2 fermion parity pump, and the entanglement-spectrum crossing for this case is protected by the conservation of fermion parity.