Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state

Abstract

We study the dynamics of the Lipkin-Meshkov-Glick (LMG) model with finite number of spins. In the thermodynamic limit, the ground state of the LMG model with isotropic Hamiltonian in broken phase breaks to a mean-field ground state with a certain direction. However, when the spins number $N$ is finite, the exact ground state is always unique and is not given by a classical mean-field ground state. Here we prove that for $N$ is large but finite, through a tiny external perturbation, a localized state which is close to a mean-field ground state can be prepared, which mimics a spontaneous symmetry breaking (SSB). Besides, we find the localized in-plane spin polarization oscillates with two different frequencies $\sim O(1/N)$, and the lifetime of the localized state is long enough to exhibit this oscillation. We numerically test the analytical results and find that they agree with each other very well. Finally, we link the phenomena to quantum time crystals and quasicrystals.

Accepted for Phys. Rev. A, 10 pages, 7 figures. Added a section of correlation function in time, and more discussion on time quasicrystal

References in corpus (7)

• Absence of Quantum Time Crystals
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• Cavity assisted single- and two-mode spin-squeezed states via phase-locked atom-photon coupling
• Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath

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