Thermal dynamics on the lattice with exponentially improved accuracy

Abstract

We present a novel simulation prescription for thermal quantum fields on a lattice that operates directly in imaginary frequency space. By distinguishing initial conditions from quantum dynamics it provides access to correlation functions also outside of the conventional Matsubara frequencies ωn=2πnT. In particular it resolves their frequency dependence between ω=0 and ω1=2πT, where the thermal physics ω∼T of e.g. transport phenomena is dominantly encoded. Real-time spectral functions are related to these correlators via an integral transform with rational kernel, so that their unfolding from the novel simulation data is exponentially improved compared to standard Euclidean simulations. We demonstrate this improvement within a non-trivial 0+1-dimensional quantum mechanical toy-model and show that spectral features inaccessible in standard Euclidean simulations are quantitatively captured.

Keywords

• Thermal quantum field theory
• Lattice simulations
• Spectral functions