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arXiv:2107.06926 · Physical review. B./Physical review. B

Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological p -wave superfluid

Aidan Zabalo, Emil A. Yuzbashyan

Published Sep 13, 2021• 1 citation
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Abstract

We study the quench dynamics of a topological $p$-wave superfluid with two competing order parameters, ${\mathrm{\ensuremath{\Delta}}}_{\ifmmode\pm\else\textpm\fi{}}(t)$. When the system is prepared in the $p+ip$ ground state and the interaction strength is quenched, only ${\mathrm{\ensuremath{\Delta}}}_{+}(t)$ is nonzero. However, we show that fluctuations in the initial conditions result in the growth of ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}(t)$ and chaotic oscillations of both order parameters. We term this behavior phase III'. In addition, there are two other types of late-time dynamics---phase I where both order parameters decay to zero and phase II where ${\mathrm{\ensuremath{\Delta}}}_{+}(t)$ asymptotes to a nonzero constant while ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}(t)$ oscillates near zero. Although the model is nonintegrable, we are able to map out the exact phase boundaries in parameter space. Interestingly, we find phase III' is unstable with respect to breaking the time-reversal symmetry of the interaction. When one of the order parameters is favored in the Hamiltonian, the other one rapidly vanishes and the previously chaotic phase III' is replaced by the Floquet topological phase III that is seen in the integrable chiral $p$-wave model.

DOI
10.1103/physrevb.104.104505

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We investigate the dynamics of a one-dimensional p-wave superconductor with next-nearest-neighbor hopping and superconducting interaction derived from a three-spin interacting Ising model in transverse field by mapping to Majorana fermions. The next-nearest-neighbor hopping term leads to a new topological phase containing two zero-energy Majorana modes at each end of an open chain, compared to a nearest-neighbor p-wave superconducting chain. We study the Majorana survival probability (MSP) of a particular Majorana edge state when the initial Hamiltonian (H_{i}) is changed to the quantum critical as well as off-critical final Hamiltonian (H_{f}), which additionally contains an impurity term (H_{imp}) that breaks the time-reversal invariance. For the off-critical quenching inside the new topological phase with H_{f}=H_{i}+H_{imp}, and small impurity strength (λ_{d}), we observe a perfect oscillation of the MSP as a function of time with a single frequency (determined by the impurity strength λ_{d}) that can be analyzed from an equivalent two-level problem. On the other hand, the MSP shows a beating like structure with time for quenching to the phase boundary separating the topological phase (with two edge Majoranas at each edge) and the nontopological phase where the additional frequency is given by inverse of the system size. We attribute this behavior of the MSP to the modification of the energy levels of the final Hamiltonian due to the application of the impurity term.