  We provide a mathematical definition of a low energy scaling limit of a
sequence of general non-relativistic quantum theories in any dimension, and
apply our formalism to anyonic chains. We formulate Conjecture 4.3 on
conditions when a chiral unitary rational (1+1)-conformal field theory would
arise as such a limit and verify the conjecture for the Ising minimal model
$M(4,3)$ using Ising anyonic chains. Part of the conjecture is a precise
relation between Temperley-Lieb generators $\{e_i\}$ and some finite stage
operators of the Virasoro generators $\{L_m+L_{-m}\}$ and $\{i(L_m-L_{-m})\}$
for unitary minimal models $M(k+2,k+1)$ in Conjecture 5.5. A similar earlier
relation is known as the Koo-Saleur formula in the physics literature [39].
Assuming Conjecture 4.3, most of our main results for the Ising minimal model
$M(4,3)$ hold for unitary minimal models $M(k+2,k+1), k\geq 3$ as well. Our
approach is inspired by an eventual application to an efficient simulation of
conformal field theories by quantum computers, and supported by extensive
numerical simulation and physical proofs in the physics literature.
