2025/12/02 by Ganguli, Maitri, Sen, Diptiman
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2512.02470
We study the effect of driving the Su-Schrieffer-Heeger model using two unitary operators U1 and U2 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 and randomly. For a periodic protocol, when U1 and U2 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 echo (LE) starting with a random initial state. We find that the LE exhibits pronounced oscillations whose Fourier transform has peaks at frequencies which agree with the most prominent gaps between pairs of quasienergies. Next, when U1 and U2 are applied in a quasiperiodic way (we consider Fibonacci and Thue-Morse protocols), we study the LE starting with an initial state which is an end mode of one of the unitaries. 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 ε2 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 U1 and U2 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.