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 ag2 according to a renormalization scheme; the authors reference a scheme with d ln(ag2) / 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 ag2 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.

References

Whether the running coupling has a non-trivial dependence on $j_{\rm max}$ should be studied analytically and tested against numerical calculations, which are left for future work.

— Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory  (2402.04221 - Turro et al., 2024) in Section 5.1 (Continuum Limit and Renormalization)

However, it is an interesting question of how large this truncation has to be to retrieve the continuum physics and whether there is some assistance provided by gauge invariance and universality in this context. For example, in one dimension, we found that one can obtain an accurate central charge even with $j_\text{max}=1/2$. We leave these questions regarding higher dimensions for future work.

— Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks  (2609.28634 - Jha et al., 23 Sep 2026) in Section 2, immediately following the discussion of the hardcore-gluon truncation

A systematic quantitative characterization of the scaling of observables with $R_{\rm max}$ and the gauge coupling $g$, particularly toward the weak-coupling regime, remains an open question.

— Particle Physics Driven by Quantum Technology - Quantum Simulations and Quantum Sensing  (2609.20500 - Bloch et al., 17 Sep 2026) in Section 2.1.1, “Gauge fields” (Hamiltonians and digitizations)