PRX Quantum (Jan 2023)

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

  • B.-W. Li,
  • Y.-K. Wu,
  • Q.-X. Mei,
  • R. Yao,
  • W.-Q. Lian,
  • M.-L. Cai,
  • Y. Wang,
  • B.-X. Qi,
  • L. Yao,
  • L. He,
  • Z.-C. Zhou,
  • L.-M. Duan

DOI
https://doi.org/10.1103/PRXQuantum.4.010302
Journal volume & issue
Vol. 4, no. 1
p. 010302

Abstract

Read online Read online

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.