Qubit regularized $O(N)$ nonlinear sigma models
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Abstract
Motivated by the prospect of quantum simulation of quantum field theories, we formulate the O(N) nonlinear sigma model as a “qubit” model with an (N + 1)-dimensional local Hilbert space at each lattice site. Using an efficient worm algorithm in the worldline formulation, we demonstrate that the model has a second-order critical point in (2 + 1) dimensions, where the continuum physics of the nontrivial O(N) Wilson-Fisher fixed point is reproduced. We compute the critical exponents ν and η for the O(N) qubit models up to N = 8, and find excellent agreement with known results in literature from various analytic and numerical techniques for the O(N) Wilson-Fisher universality class. Our models are suited for studying O(N) nonlinear sigma models on quantum computers up to N = 8 in d = 2, 3 spatial dimensions.