Large Nc Truncations for SU(Nc) Lattice Yang-Mills Theory with Fermions

TL;DR

This paper introduces a novel truncation scheme for lattice QCD with fermions suitable for quantum simulations, enabling more efficient modeling of gauge fields and fermions on quantum computers.

Contribution

It presents a new truncation method combining local Krylov basis, electric energy limits, fermion number constraints, and large N_c scaling truncation for lattice QCD.

Findings

Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are provided.

Numerical simulations demonstrate string-breaking dynamics with the truncated models.

Abstract

Quantum simulations of quantum chromodynamics (QCD) require a representation of gauge fields and fermions on the finitely many degrees of freedom available on a quantum computer. We introduce a truncation of lattice QCD coupled to staggered fermions that includes (i) a local Krylov truncation that generates allowed basis states; (ii) a maximum allowed electric energy per link; (iii) a limit on the number of fermions per site; and (iv) a truncation in the large N_c scaling of Hamiltonian matrix elements. Explicit truncated Hamiltonians for 1+1D and 2+1D lattices are given, and numerical simulations of string-breaking dynamics are performed.