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Qubit Regularization of Asymptotic Freedom.

Tanmoy Bhattacharya1, Alexander J Buser1,2, Shailesh Chandrasekharan3

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Researchers demonstrate a quantum lattice Hamiltonian, the Heisenberg comb, for regularizing the (1+1)-dimensional nonlinear O(3) sigma model. This method shows promise for quantum computers to exhibit asymptotic freedom.

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Area of Science:

  • Quantum Field Theory
  • Condensed Matter Physics
  • Quantum Information

Background:

  • The (1+1)-dimensional nonlinear O(3) sigma model is a fundamental model in quantum field theory.
  • Regularizing this model is crucial for theoretical studies and potential applications.
  • Previous methods faced challenges in achieving large correlation lengths and demonstrating asymptotic freedom.

Purpose of the Study:

  • To introduce and validate a novel quantum lattice Hamiltonian, the
  • Heisenberg comb,
  • for regularizing the (1+1)-dimensional nonlinear O(3) sigma model.
  • To explore the potential of near-term quantum computers in demonstrating asymptotic freedom.
  • To investigate the emergence of the continuum limit from a quantum lattice description.

Main Methods:

  • Implementation of a quantum lattice Hamiltonian (Heisenberg comb) acting on a two-qubit Hilbert space per site.
  • Utilizing a world-line Monte Carlo method to simulate the model.
  • Developing a quantum circuit description for the time evolution.

Main Results:

  • The Heisenberg comb successfully reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 lattice units.
  • Strong evidence is provided for the model's ability to regularize the (1+1)-dimensional nonlinear O(3) sigma model.
  • The study outlines a pathway for the emergence of the continuum limit.

Conclusions:

  • The Heisenberg comb offers a viable and efficient method for regularizing the (1+1)-dimensional nonlinear O(3) sigma model.
  • Near-term quantum computers may be capable of simulating this model and demonstrating asymptotic freedom.
  • This work bridges quantum field theory and quantum computation, opening new avenues for research.