Probing Critical Behavior of Long-Range Transverse-Field Ising Model through Quantum Kibble-Zurek Mechanism

Abstract

The trapped-ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena, such as quantum phase transition, localization, thermalization, and information propagation. For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters. Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism. By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite-size effect. For ferromagnetic interaction, our experimental result agrees with the previous numerical prediction. As for the antiferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory.1 MoreReceived 17 August 2022Accepted 20 December 2022DOI:https://doi.org/10.1103/PRXQuantum.4.010302Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCritical exponentsMagnetic orderQuantum information with trapped ionsQuantum simulationPhysical SystemsTrapped ionsQuantum InformationAtomic, Molecular & Optical