Operator product expansion for radial lattice quantization of 3D ϕ4 theory

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3D Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the quantum finite elements method to implement radially quantized critical <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>ϕ</a:mi><a:mn>4</a:mn></a:msup></a:math> theory on simplicial lattices approaching <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="double-struck">R</c:mi><c:mo>×</c:mo><c:msup><c:mi>S</c:mi><c:mn>2</c:mn></c:msup></c:math>. Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi mathvariant="normal">Δ</f:mi><f:mi>ε</f:mi></f:msub></f:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi mathvariant="normal">Δ</i:mi><i:mi>T</i:mi></i:msub></i:math> as well as ratios of the operator product expansion coefficients <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>f</l:mi><l:mrow><l:mi>σ</l:mi><l:mi>σ</l:mi><l:mi>ε</l:mi></l:mrow></l:msub></l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>f</n:mi><n:mrow><n:mi>σ</n:mi><n:mi>σ</n:mi><n:mi>T</n:mi></n:mrow></n:msub></n:math> of the first spin-0 and spin-2 primary operators <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>ε</p:mi></p:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>T</r:mi></r:math> of the 3D Ising CFT.