<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>θ</mml:mi> </mml:math> -vacuum from functional renormalization

We study topological properties of a quantum mechanical system with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> symmetry within the functional renormalization group approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically, we embed the original symmetry into the complex plane, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>1</e:mn> <e:mo stretchy="false">)</e:mo> <e:mo stretchy="false">→</e:mo> <e:mi mathvariant="double-struck">C</e:mi> </e:math> . We compute the effective potential of a given topological sector by restricting ourselves to field configurations with given generalized nontrivial Chern-Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schrödinger equation.