Uncertain behavior of larger truncations with n_p ≠ n_l

Determine whether truncations of the SU(N_c) Kogut–Susskind Hamiltonian labeled by (n_p, n_l, k) with n_p ≠ n_l exhibit the same anomalous behavior observed for the (1,2,2) truncation in SU(3) lattice gauge theory in 2+1 dimensions, specifically disagreement with untruncated calculations and a larger frozen lattice spacing that prevents approaching the continuum limit.

Background

The paper introduces Krylov-inspired local truncations of the electric basis for SU(N_c) lattice gauge theory, denoted by (n_p, n_l, k), and evaluates their performance via tensor-network simulations in 2+1D SU(3). While most low-lying truncations agree with traditional lattice calculations down to comparatively small couplings, the (1,2,2) truncation unexpectedly fails to agree and appears to freeze the lattice spacing at larger values.

This anomalous behavior is linked to proximity to a theory-space point with vanishing correlation length (as shown by effective mass studies and Appendix A). The authors therefore raise the explicit question of whether similar issues arise for more general truncations where the number of allowed plaquette applications differs from the number of link applications (n_p ≠ n_l), motivating further investigation of truncation structure and scaling behavior.