HHIQCD2024

Formulation of SU(N) Lattice Gauge Theories with Schwinger Fermions

Nov 15, 2024, 4:30 PM

30m

Panasonic Auditorium, Yukawa Hall (YITP)

5th week (Formal developments and other frontiers in lattice QCD) Seminar (5th week)

Speaker

Hanqing Liu (Los Alamos National Laboratory)

Description

The recent advancements towards scalable fault-tolerant quantum computing have brought excitement about simulating lattice gauge theories on quantum computers. However, digital quantum computers require truncating the infinite-dimensional link Hilbert space to finite dimensions. In this talk, we focus on the $\mathrm{SU}(N)$ gauge theory coupled to $N_f$ flavor of quarks and propose a formulation of the gauge field using Schwinger fermions. Remarkably, the resulting theory can be expressed purely in terms of gauge-invariant operators. This formulation applies to any $\mathrm{SU}(N)$ gauge group in any spacetime dimension. To explore the potential for reproducing the continuum physics, we study this model at $N=2$ in two spacetime dimensions, where the low-energy continuum physics is expected to be described by a coset Wess-Zumino-Witten (WZW) model. Using tensor network methods, we find that the critical theory can indeed be understood as an $\mathrm{SU}(2{)}_1$ WZW model.

Presentation materials

slides.pdf