Qubit regularization of asymptotic freedom

• URL: http://arxiv.org/abs/2012.02153v2
• Date: Tue, 27 Apr 2021 16:14:48 GMT
• Title: Qubit regularization of asymptotic freedom
• Authors: Tanmoy Bhattacharya (1), Alexander J. Buser (2 and 1), Shailesh Chandrasekharan (3), Rajan Gupta (1), Hersh Singh (4 and 3) ((1) Los Alamos National Laboratory, Los Alamos, NM, USA, (2) Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA, (3) Department of Physics, Duke University, Durham, NC, USA, (4) Institute for Nuclear Theory, University of Washington, Seattle, WA, USA)
• Abstract summary: Heisenberg-comb acts on a Hilbert space with only two qubits per spatial lattice site. We show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units. We argue that near-term quantum computers may suffice to demonstrate freedom.
• Score: 35.37983668316551
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide strong evidence that the asymptotically free (1+1)-dimensional non-linear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the "Heisenberg-comb", that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg-comb consists of a spin-half anti-ferromagnetic Heisenberg-chain coupled anti-ferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of time-evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.

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