Qubit regularized O(N) nonlinear sigma models

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 $\ensuremath{\nu}$ and $\ensuremath{\eta}$ 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.