Universality of a truncated sigma-model

Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in computers with number of qubits. A truncation the is then needed and physical results are obtained after double limit: one to remove another regulator (the continuum limit). simpler alternative find model belonging same universality class as (a "qubitization"), so only limit required. qubitization $1+1$ asymptotically free $O(3)$ nonlinear $\sigma$-model based on ideas non-commutative geometry was previously proposed arXiv:1903.06577 this paper, we provide evidence that it reproduces physics both infrared ultraviolet regimes.