Precision estimates of large charge RG exponents <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> in the 3D XY universality class

We accurately compute the renormalization group (RG) exponents <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>Y</a:mi> <a:mi>q</a:mi> </a:msub> </a:math> of large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>q</c:mi> </c:math> fields at the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>O</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>2</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> invariant fixed point in three dimensions. We build on an iterative approach that has been previously proposed and is implemented by using the worm algorithm. We simulate an improved XY model, that has next-to-next-to-nearest couplings in addition to nearest ones. In the worm update we incorporate weights, which allows us to obtain accurate results up to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>q</i:mi> <i:mo>=</i:mo> <i:mn>64</i:mn> </i:math> . For example we get <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>Y</k:mi> <k:mi>q</k:mi> </k:msub> <k:mo>=</k:mo> <k:mn>1.76370</k:mn> <k:mo stretchy="false">(</k:mo> <k:mn>12</k:mn> <k:mo stretchy="false">)</k:mo> </k:math> , 0.89167(23), and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mo>−</o:mo> <o:mn>0.11203</o:mn> <o:mo stretchy="false">(</o:mo> <o:mn>34</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>q</s:mi> <s:mo>=</s:mo> <s:mn>2</s:mn> </s:math> , 3, and 4, respectively. The comparison with the large <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>q</u:mi> </u:math> effective field theory gives an excellent agreement down to <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>q</w:mi> <w:mo>=</w:mo> <w:mn>4</w:mn> </w:math> and provides accurate estimates of the parameters of the effective field theory.