Quantum Simulation of the Universal Features of the Polyakov Loop.

Area of Science:

• High-energy physics
• Quantum simulation
• Condensed matter physics

Background:

• Lattice gauge theories are crucial for high-energy physics.
• Experimental quantum simulation of these theories faces significant challenges.
• The Abelian Higgs model in 1+1 dimensions is explored as a potential platform.

Purpose of the Study:

• To identify a suitable experimental platform for quantum simulation of lattice gauge theories.
• To develop a theoretical framework connecting numerical and Hamiltonian formulations.
• To propose a specific experimental setup using ultracold atoms.

Main Methods:

• Discrete tensor reformulation to bridge numerical and Hamiltonian formulations.
• Investigation of nonzero charge sectors via Polyakov loop and external electric field.
• Analysis of universal functions invariant under temporal lattice spacing changes.

Main Results:

• The Abelian Higgs model in 1+1D is identified as a prime candidate for quantum simulation.
• Universal relationships between mass gap, gauge coupling, and spatial size were found.
• A method to probe nonzero charge sectors was successfully demonstrated.

Conclusions:

• The proposed theoretical framework enables analog quantum simulation of lattice gauge theories.
• Ultracold atoms in optical lattices with Rydberg interactions offer a viable experimental approach.
• This work provides a pathway for simulating fundamental physics with quantum systems.