The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators

Abstract

We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick (LMG) model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization are fragile, and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs. those that depend on local trajectories.

13 pages, 7 figures

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• Eigenstate entanglement in integrable collective spin models
• Late-time critical behavior of local string-like observables under quantum quenches
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
• "Bound luminosity" state in the extended Dicke model
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Lasing and counter-lasing phase transitions in a cavity QED system
• Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model