Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks

Area of Science:

• * Fundamental particle physics and quantum field theory.
• * Computational physics and condensed matter theory.

Background:

• * Gauge theories are crucial for understanding matter and interactions.
• * Non-perturbative effects and phase diagrams, especially at finite charge density, remain challenging due to the sign-problem in numerical simulations.

Purpose of the Study:

• * To apply Tensor Network methods for sign-problem-free simulations of lattice gauge theories.
• * To investigate the ground states and phase diagram of compact Quantum Electrodynamics (QED) with dynamical matter.
• * To explore collective phases, confinement, and charge-screening effects at zero and finite charge densities.

Main Methods:

• * Employed Tensor Network simulations in the Hamiltonian formulation.
• * Simulated a three-dimensional lattice gauge theory including dynamical matter.
• * Addressed sign-problem limitations inherent in traditional Monte Carlo methods.

Main Results:

• * Successfully simulated ground states of compact QED using a sign-problem-free approach.
• * Characterized collective phases of the model at varying charge densities.
• * Investigated the presence of a confining phase at large gauge coupling and analyzed charge-screening effects.

Conclusions:

• * Tensor Network simulations provide a viable, sign-problem-free alternative for studying gauge theories with dynamical matter.
• * The study offers new insights into the phase structure and properties of compact QED, particularly at finite densities.
• * This methodology opens avenues for exploring complex non-perturbative phenomena in quantum field theory.