j_max dependence of the running coupling in 2+1D SU(2) Hamiltonian lattice gauge theory

Determine whether the renormalization group running of the dimensionless coupling ag^2 in the 2+1-dimensional SU(2) Hamiltonian lattice gauge theory depends non-trivially on the local Hilbert space truncation parameter j_max as the lattice spacing a approaches zero, and, if so, characterize this dependence analytically and validate it with numerical calculations along the continuum limit trajectory.

Background

Taking the continuum limit in 2+1D SU(2) lattice gauge theory requires tuning the coupling ag^2 according to a renormalization scheme; the authors reference a scheme with d ln(ag^2) / d ln a = 1. In the Hamiltonian approach, computations also employ a local Hilbert space truncation labeled by j_max, which could, in principle, affect renormalization behavior.

The authors emphasize that, beyond the standard running with a, potential dependence of ag^2 on j_max has not been established and would need both analytical derivations and numerical verification. In this work, they only account for coupling renormalization and defer any investigation of additional renormalization effects tied to j_max.