Dynamics of a quantum phase transition in the Aubry-Andr\'{e}-Harper model with $p$-wave superconductivity
| Autor: | Ye-Ming Meng, Gao Xianlong, Chaohong Lee, Xunda Jiang, Xianqi Tong, Gentil Dias de Moraes Neto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Quantum phase transition
Superconductivity Physics Phase transition Quantum Physics Condensed matter physics 02 engineering and technology Condensed Matter - Disordered Systems and Neural Networks 021001 nanoscience & nanotechnology 01 natural sciences symbols.namesake Condensed Matter - Strongly Correlated Electrons 0103 physical sciences Exponent symbols Initial value problem 010306 general physics 0210 nano-technology Hamiltonian (quantum mechanics) Critical exponent Scaling |
| Popis: | We investigate the nonequilibrium dynamics of the one-dimension Aubry-Andr\'{e}-Harper model with $p$-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from localized phase to critical phase by linearly decreasing the potential strength $V$. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent $z\nu$, giving the correlation length $\nu=0.997$ and dynamical exponent $z=1.373$, which are different from the Aubry-Andr\'{e} model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of $V=0$ and $V=\infty$, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of the quench is the same as one of the two limits mentioned before, and similar behaviors will occur. Comment: 9 pages, 7 figures |
| Databáze: | OpenAIRE |
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