Jesse Stryker, LBL
The loop-string-hadron (LSH) approach to lattice gauge theories is a Hamiltonian formulation in which the elementary degrees of freedom are gauge invariant and defined locally, with the non-Abelian Gauss’s laws being traded in favor of Abelian flux constraints. This formulation is being pursued as a candidate for quantum simulation and tensor network studies. Originally, the LSH approach was developed for the SU(2) gauge group in any number of spatial dimensions, with coupling to staggered quarks [PRD 101, 114502 (2020)]. Generalizing the approach to SU(3) is crucial if it is to have any application for QCD, and a solution for one-dimensional space was published recently [PRD 107, 094513 (2023)]. In multidimensional space, it turns out, the SU(3) generalization involves fundamentally new challenges. In this talk, I discuss the SU(3)-invariant Hilbert space of a single (trivalent) lattice site, the characterization of the physical degrees of freedom, and issues of nonorthogonality. Our proposal for how to construct an orthogonal basis is self-contained and requires no knowledge of SU(3) Clebsch-Gordon coefficients; however, closed-form expressions have only been found for a subset of states. I will conclude by sharing the current direction of this program.