Fragility to quantum fluctuations of classical Hamiltonian period doubling

TL;DR

This paper investigates how quantum fluctuations affect a classical period-doubling Hamiltonian time crystal, revealing that quantum effects destabilize persistent period doubling, with the classical symmetry breaking being fragile to quantum tunneling.

Contribution

It introduces a quantum version of a classical Hamiltonian time crystal, analyzing the impact of quantum fluctuations and tunneling on time-translation symmetry breaking.

Findings

Quantum fluctuations destroy persistent period doubling.

Rabi oscillations indicate the absence of time-translation symmetry breaking at finite spin size.

Classical chaos properties are mirrored in the quantum model in the large system limit.

Abstract

We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. 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 $N\to\infty$ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos. For $N\to\infty$, and $l$ finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for $l\to\infty$ 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 $l$ 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.