Qubit $O(N)$ nonlinear sigma models
Hersh Singh · arXiv (Cornell University) · 2019
We reformulate the traditional lattice $O(N)$ nonlinear sigma models as qubit models with a $N+1$ dimensional Hilbert space at each lattice site. Using an efficient worm algorithm in the worldline formulation, we demonstrate that the model has a quantum critical point in $(2+1)$ dimensions. We compute the critical exponents $ u$ and $\eta$ up to $N=8$. By comparing these exponents with results from large-$N$ and $\epsilon$-expansions, we demonstrate that these quantum critical points lie in the usual $O(N)$ Wilson-Fisher universality class. Our models are suited for studying $O(N)$ Wilson-Fisher universality class on quantum computers up to $N=8$.