Fragility to quantum fluctuations of classical Hamiltonian period doubling
arXiv:2108.11408 · doi:10.1103/PhysRevB.104.134309
Abstract
We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the classical interacting angular momenta with quantum spins of size . The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size. In the thermodynamic limit the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite- quantum chaos. For , and finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Our results show the instability of time-translation symmetry breaking in this classical system even to the smallest quantum fluctuations, because of tunneling effects.
arXiv comment15 pages and 9 figures
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