Exact solutions and Dynamical phase transitions in the Lipkin-Meshkov-Glick model with Dual nonlinear interactions
arXiv:2310.14244 · doi:10.1016/j.aop.2026.170344
Abstract
Lipkin-Meshkov-Glick (LMG) model is paradigmatic to study quantum phase transition in equilibrium or non-equilibrium systems and entanglement dynamics in a variety of disciplines. The generic LMG model usually incorporates two nonlinear interactions. While the classical dynamics of the single-nonlinear-inteaction LMG model is well understood through Jacobi elliptic functions, the dualinteraction case remains unexplored due to analytical challenges. Here, by constructing an auxiliary function that maps the dynamics to the complex plane of Jacobi elliptic functions, we derive exact solutions of classical dynamics for the dual-interaction LMG model. Based on the exact solutions, we give the classical dynamical phase diagram of the LMG model with dual nonlinear interactions, and find out a non-logarithmic behavior of dynamical criticality which is absent in case of single nonlinear interaction. Our results establish a benchmark to analyze the quantum dynamical phase transitions and many-body entanglement dynamics of finite-size LMG model.
18 pages, 10 figures, 1 table
References in corpus (31)
- Nonequilibrium dynamics of closed interacting quantum systems
- Quantum metrology with nonclassical states of atomic ensembles
- The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Quantum spin squeezing
- Classical bifurcation at the transition from Rabi to Josephson dynamics
- Many particle entanglement in two-component Bose-Einstein Condensates
- Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
- The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
- Exploring dynamical phase transitions with cold atoms in an optical cavity
- Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
- Casimir forces in binary liquid mixtures
- Probing the dynamical phase transition with a superconducting quantum simulator
- Entanglement dynamics in the Lipkin-Meshkov-Glick model
- Dissipation-induced anomalous multicritical phenomena
- Generation of many-particle entanglement in an ion trap by adiabatic ground-state transitions
- Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
- Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
- Chaotic dynamical ferromagnetic phase induced by non-equilibrium quantum fluctuations
- Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm
- Excited-state quantum phase transitions and periodic dynamics
- Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity
- Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state
- AC-driven Quantum Phase Transition in the Lipkin-Meshkov-Glick Model
- Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
- Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model
- Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions
- Simulation of XXZ Spin Models using Sideband Transitions in Trapped Bosonic Gases
- Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model
- Coherent Quantum Dynamics: What Fluctuations Can Tell
- Coherent state approach to the cross collisional effects in the population dynamics of a two-mode Bose-Einstein condensate