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

TL;DR

The paper develops a gauge-invariant truncation framework for SU($N_c$) lattice Yang–Mills theory with fermions, enabling real-time simulations relevant to QCD on quantum devices. By combining Krylov subspace truncations, per-link electric-energy cutoffs, per-site fermion cutoffs, and a controlled large-$N_c$ expansion, the authors construct explicit truncated Hamiltonians in 1+1D and 2+1D and study real-time string dynamics, vacuum, and meson-like excitations. They uncover fidelity revivals reminiscent of quantum many-body scars and show that string breaking is dynamically suppressed in the large-$N_c$ limit, consistent with theoretical expectations. The work provides a practical route to simulate non-Abelian lattice gauge theories in regimes that are challenging for classical methods and establishes a foundation for future quantum hardware implementations of QCD-like dynamics.

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.

Figures (33)

• Figure 1: Example data that participates in the Kogut-Susskind model on a square lattice. Blue indicates a Wilson loop for plaquette $p$. Green indicates a Wilson line and lattice sites for hopping operator at link $\ell$. The odd and even endpoints of $\ell$ are indicated as $\ell^+$ and $\ell^-$. The notation $\ell^+$, $\ell^-$ can also be used for the half-links of $\ell$ attached to these respective endpoints (residing on each side of the dotted line that cuts link $\ell$).
• Figure 2: Example polyhex tile that can be used to generate the full hexagonal lattice structure obtained by point-splitting a square lattice. White sites are fermion-like and black sites are anti-fermion-like.
• Figure 3: Illustration of double-vertex cuts associated with a generic hopping transition at arbitrary link $\ell \in \mathcal{E}$. The odd and even endpoints of $\ell$ are labeled $x$ and $y$, respectively. Odd sites are indicated with a black vertex, and even sites are indicated with a white vertex. Hopping acts on sites $x$ and $y$, as well as link $\ell$, but subsequently intertwines the irreps on all external legs into new singlets. In (a), two neighboring sites and their half-links are shown as a subgraph in a non-point-split lattice. In (b), point-splitting is performed only around link $\ell$ to yield the simplified subgraph that participates in hopping transitions at link $\ell$.
• Figure 4: Transition allowed at $T_1$: $\ket{\mathbf{1},\mathbf{1},\mathbf{1}}\to\ket{\mathbf{1},\mathbf{N},\mathbf{1}}$.
• Figure 5: New transition at $T_2$: $\ket{\mathbf{N},\mathbf{1},\mathbf{N}}\to\ket{\mathbf{N},\overline{\mathbf{N}},\mathbf{N}}$.