Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols
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arXiv
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2025
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| author | Ganguli, Maitri Sen, Diptiman |
| author_facet | Ganguli, Maitri Sen, Diptiman |
| contents | We study the effect of driving the Su-Schrieffer-Heeger model using two unitary operators $U_1$ and $U_2$ in different combinations; the unitaries differ in the values of the inter-cell hopping amplitudes. Specifically, we study the cases where the unitaries are applied periodically, quasiperiodically, aperiodically and randomly. For a periodic protocol, when $U_1 = e^{-i H_1 T/2}$ and $U_2 = e^{-i H_2 T/2}$ are applied alternately, we find that end modes may appear, but the number of end modes does not always agree with the winding number which is a $Z$-valued topological invariant. We then study the Loschmidt amplitude ($LA$) starting with a initial state which is an end mode of $H_1$. We find that the $LA$ exhibits pronounced oscillations whose Fourier transform has a peak at a frequency which is equal to the quasienergy of an end mode of $U$. Next, when $U_1$ and $U_2$ are applied in a quasiperiodic or aperiodic way (we consider the Fibonacci and Thue-Morse protocols as examples), we study the Loschmidt echo ($LE$) starting with an initial state which is an end mode of the Hamiltonian $H_1$. When the inter-cell hoppings differ by a small amount denoted by $ε$, and the time period $T$ of each unitary is also small, the distance between the unitaries is found to be proportional to $εT$. We then find that the $LE$ oscillates around a particular value for a very long time before decaying to zero. The deviation of the value of the $LE$ from 1 scales as $ε^2$ for a fixed value of $T$, while the time after which the $LE$ starts decaying to zero has an interesting dependence on $ε$ and $T$. Finally, when $U_1$ and $U_2$ are applied in a random order, the $LE$ rapidly decays to zero with increasing time. We have presented a qualitative understanding of the above results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_02470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols Ganguli, Maitri Sen, Diptiman Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics We study the effect of driving the Su-Schrieffer-Heeger model using two unitary operators $U_1$ and $U_2$ in different combinations; the unitaries differ in the values of the inter-cell hopping amplitudes. Specifically, we study the cases where the unitaries are applied periodically, quasiperiodically, aperiodically and randomly. For a periodic protocol, when $U_1 = e^{-i H_1 T/2}$ and $U_2 = e^{-i H_2 T/2}$ are applied alternately, we find that end modes may appear, but the number of end modes does not always agree with the winding number which is a $Z$-valued topological invariant. We then study the Loschmidt amplitude ($LA$) starting with a initial state which is an end mode of $H_1$. We find that the $LA$ exhibits pronounced oscillations whose Fourier transform has a peak at a frequency which is equal to the quasienergy of an end mode of $U$. Next, when $U_1$ and $U_2$ are applied in a quasiperiodic or aperiodic way (we consider the Fibonacci and Thue-Morse protocols as examples), we study the Loschmidt echo ($LE$) starting with an initial state which is an end mode of the Hamiltonian $H_1$. When the inter-cell hoppings differ by a small amount denoted by $ε$, and the time period $T$ of each unitary is also small, the distance between the unitaries is found to be proportional to $εT$. We then find that the $LE$ oscillates around a particular value for a very long time before decaying to zero. The deviation of the value of the $LE$ from 1 scales as $ε^2$ for a fixed value of $T$, while the time after which the $LE$ starts decaying to zero has an interesting dependence on $ε$ and $T$. Finally, when $U_1$ and $U_2$ are applied in a random order, the $LE$ rapidly decays to zero with increasing time. We have presented a qualitative understanding of the above results. |
| title | Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols |
| topic | Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2512.02470 |